A ball is thrown vertically upward with a speed of 40 m/s. The time taken by the ball to reach the maximum height would be approximately

examrobotsa's picture

Submitted by examrobotsa on

Q: 19 (NDA-I/2022)
A ball is thrown vertically upward with a speed of 40 m/s. The time taken by the ball to reach the maximum height would be approximately

question_subject: 

Maths

question_exam: 

NDA-I

stats: 

0,17,22,5,11,17,6

keywords: 

{'maximum height': [0, 0, 0, 1], 'ball': [1, 3, 13, 12], 'speed': [0, 1, 2, 0], 'time': [2, 6, 15, 23]}

The correct answer is option 3, 4 seconds.

To understand why, let`s analyze the motion of the ball. When the ball is thrown vertically upward, its initial velocity is 40 m/s. The acceleration due to gravity acts in the opposite direction, causing the ball to slow down until it reaches its highest point. At the highest point, the ball momentarily stops moving upward before coming back down.

The time taken to reach the maximum height can be determined using the equation for vertical motion:

v = u + at

Where:

v is the final velocity (which is zero at the highest point),

u is the initial velocity (40 m/s),

a is the acceleration due to gravity (-9.8 m/s^2), and

t is the time taken.

Rearranging the equation, we can solve for t:

0 = 40 - 9.8t

Simplifying, we find t = 40 / 9.8 ≈ 4 seconds.

Therefore, it takes approximately 4 seconds for the ball to reach the maximum height.