Question

A ball is dropped from a building of height 100m. At the same time, another ball is then thrown vertically up from the ground with a velocity V_0.  They meet each other at the middle. What is the speed V₀ of the ball thrown vertically up?

a) 44.3m/s

b)9.8m/s

c) 31.3m/s

d)19.6 m/s

e) 98.0m/s

Answer 1

if the balls meet at the middle that means their distance traveled is equal which is 50 m.

now for the ball dropped from the building,

using second equation of motion,

s = u*t + (0.5)*a*t²

where u is its initial velocity and t is the time taken to reach at the middle of the building.

given :- u = 0 m/s ; s = 50 m ; a = 9.8 m/s²

now putting all the known values,

50 = 0 + (0.5)*9.8*t²

solving for t,

t² = 10.2

t = 3.2 s

so that means both the balls traveled for 3.2 seconds.

now using the second equation of motion for the ball which thrown vertically upwards.

s = U*t + (0.5)*A*t²

where U and A are the initial velocity amd acceleration of the ball which thrown upwards.

given:- s = 50 m ; t = 3.2 s ; A = -9.8 m/s²

now putting all the values,

50 = U * 3.2 + (0.5)*(-9.8)*3.2²

solving for U,

U = 99.98/3.2

U = 31.3 m/s

so, the correct answer is (C) 31.3 m/s.

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