A body is projected vertically upwards with a velocity of 40 m/s from a truck moving horizontally with velocity V. At the end of time of flight of the body the distance covered by the truck is 128 m. Find V   ( g=10m/s²)

Explanation

• Initial velocity (u) = 40 m/s (upward).
• Acceleration due to gravity (g) = 10 m/s² (downward).
• The time of flight (t) is the total time the object stays in the air, which can be calculated using the formula for vertical motion:

The body will first go up and then come down. The time to reach the maximum height can be found using the equation:

v = u - gt

At the maximum height, the final velocity (v) becomes 0. Thus:

0 = 40 - 10t

Solving for t:

t = 40 / 10 = 4 seconds (time to reach maximum height)

The total time of flight is twice this time (as the time to come back down is equal to the time to go up):

T = 2t = 2 × 4 = 8 seconds

• The truck moves horizontally with velocity V, and the horizontal distance traveled by the truck during the time of flight is 128 meters.
• The distance traveled by the truck is given by:

Distance = V × T

We are given that the distance covered by the truck is 128 m, and the time of flight is 8 seconds. So:

128 = V × 8

Solving for V:

V = 128 / 8 = 16 m/s

Final Answer:

The velocity of the truck V is 16 m/s.