Height, Range and Time of Flight

Height, Range and Time of Flight MDCAT MCQs with answers

20 past paper MCQs on Height, Range and Time of Flight, from the Force and Motion unit of MDCAT Physics. The year each question appeared is shown where known; tap “Show answer” for the correct option and a short solution.

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1.The range of a projectile will be maximum if the factor $\sin2\theta$ becomes: (MDCAT 2024)

  1. zero
  2. 1
  3. $1/2$
  4. $-1$
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Correct answer: (b) 1

$R=v^2\sin2\theta/g$ is largest when $\sin2\theta=1$, that is at $\theta=45^\circ$.

2.If the horizontal range of a projectile becomes half of its maximum possible horizontal range, the probable angle of projection is; (UHS MDCAT 2025)

  1. 15º
  2. 30º
  3. 45º
  4. 60º
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Correct answer: (a) 15º

The range is largest at $45^{\circ}$, and half of it needs $\sin2\theta=0.5$, so $\theta$ is $15^{\circ}$.

3.Angle at which maximum range of projectile is achieved? (NUMS MDCAT 2025)

  1. 0°
  2. 45°
  3. 90°
  4. 76°
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Correct answer: (b) 45°

The range goes as $\sin2\theta$, which is largest at $\theta=45^{\circ}$.

4.A body is projected with speed v making an angle θ with the horizontal and covers horizontal range R. If its speed is doubled, the new range will be: (SIBA MDCAT 2025)

  1. R/2
  2. R
  3. 2R
  4. 4R
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Correct answer: (d) 4R

The range goes as the square of the speed, so doubling the speed gives four times the range.

5.Two balls thrown with equal speeds but at different angles cover equal horizontal distance. If one is thrown at an angle of 40°, then the angle of projection of the other is: (SZABMU MDCAT 2025)

  1. 20°
  2. 30°
  3. 45°
  4. 50°
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Correct answer: (d) 50°

Two angles adding to $90^{\circ}$ give the same range, so the other is $50^{\circ}$.

6.The range of projectile will be maximum if the factor sin2θ becomes (UHS MDCAT 2024)

  1. Zero
  2. 1
  3. -1
  4. 2
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Correct answer: (b) 1

$R=v^2\sin2\theta/g$ is largest when the sine is one.

7.In projectile motion for which angle maximum height is half of its range? (NUMS MDCAT 2024)

  1. 73°
  2. 65°
  3. 63°
  4. 68°
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Correct answer: (c) 63°

$H=R/2$ gives $\tan\theta=2$, so the angle is about $63^{\circ}$.

8.Horizontal range of projectile will be maximum when: (NUMS MDCAT 2024)

  1. Sinθ = 1/2
  2. Sin2θ = 1
  3. Sinθ = 0
  4. Sin2θ = 0
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Correct answer: (b) Sin2θ = 1

$R=v^2\sin2\theta/g$ is largest when $\sin2\theta$ is one.

9.At what pair of angles for a projectile, the ranges are equal? (SZABMU MDCAT 2023)

  1. 20O, 60O
  2. 60O, 30O
  3. 40O, 60O
  4. 25O, 55O
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Correct answer: (b) 60O, 30O

Two angles adding to $90^{\circ}$ give the same range.

10.The angle of projection of a projectile for which its maximum height and horizontal range are equal is: (SZABMU MDCAT 2023)

  1. 86O
  2. 46 O
  3. 66 O
  4. 76 O
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Correct answer: (d) 76 O

$H=R$ gives $\tan\theta=4$, so the angle is about $76^{\circ}$.

11.Range of a projectile on a horizontal plane is same for the following pair of angle: (NUMS MDCAT 2023)

  1. 15 & 30
  2. 60 & 20
  3. 75 & 15
  4. 50 & 25
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Correct answer: (c) 75 & 15

Two angles adding to $90^{\circ}$ give the same range, and $75+15$ is the only such pair.

12.The horizontal range is 4√3 times of the maximum height. Its angle of projection is: (PMC MDCAT 2022)

  1. 90 degrees
  2. 45 degrees
  3. 60 degrees
  4. 30 degrees
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Correct answer: (d) 30 degrees

$R=4\sqrt3H$ gives $\tan\theta=4/(4\sqrt3)$, so $\theta$ is $30^{\circ}$.

13.At what angle of projectile horizontal range is minimum: (PMC MDCAT 2022)

  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 90 degrees
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Correct answer: (d) 90 degrees

$\sin2\theta$ is zero at $90^{\circ}$, so the projectile goes straight up and comes straight down.

14.For a projectile at angle (45+θ) and (45-θ), the ratio of horizontal range described by the projectile is: (PMC MDCAT 2022)

  1. 1.00
  2. 0.50
  3. 2.00
  4. 0.08
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Correct answer: (a) 1.00

The two angles add to $90^{\circ}$, so their ranges are equal and the ratio is one.

15.The projectile motion covers maximum range: (PMC MDCAT 2022)

  1. Horizontally
  2. Vertically
  3. Tangentially
  4. Linearly
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Correct answer: (a) Horizontally

The range of a projectile is measured along the horizontal.

16.If a particle launched with 5m/s at angle of 45 degree, then time of flight is: (PMC MDCAT 2022)

  1. 1.44 s
  2. 0.72 s
  3. 0.6 s
  4. 0.5 s
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Correct answer: (b) 0.72 s

$T=2u\sin\theta/g=2\times5\times0.707/9.8$, about $0.72\,\mathrm{s}$.

17.Q.78 In projectile motion, the rage of projectile will be maximum at an angle of: (NUMS MDCAT 2022)

  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 90 degrees
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Correct answer: (b) 45 degrees

The range goes as $\sin2\theta$, which is largest at $45^{\circ}$.

18.Which of the following pair of angles have same rang for a projectile? (NUMS MDCAT 2022)

  1. 10° and 20°
  2. 75° and 15°
  3. 45° and 60°
  4. 0° and 30°
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Correct answer: (b) 75° and 15°

Two angles adding to $90^{\circ}$ give the same range.

19.At what angle of projection of a projectile the range becomes half of its maximum value? (PMC MDCAT 2020)

  1. 15
  2. 20
  3. 30
  4. 40
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Correct answer: (a) 15

Half the maximum range needs $\sin2\theta=0.5$, so $\theta$ is $15^{\circ}$.

20.The range Of the projectile depends upon the velocity of the projection and the angle of the projection i.e 45. For a fixed velocity, when the angle of projection is larger than 45. Which of the following is correct? (UHS MDCAT 2019)

  1. The height attained by the projectile will be more but the range is less
  2. Both the height and the range attained by the projectile will be more.
  3. The height attained by the projectile will be less but the range is more.
  4. Both the height and the range attained by the projectile will be less.
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Correct answer: (a) The height attained by the projectile will be more but the range is less

Above $45^{\circ}$ more of the velocity goes into the vertical, so the projectile rises higher but lands nearer.

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