Question

A squirrel throws a nut from a treetop 19.6 m high. 1 second later, it throws a second nut. With what initial velocity must the second nut be thrown if it is to reach the ground at the same time as the first? with Diagram.

Answer 1

h = 19.6m (consider g = 9.8 m/s2)

at t= 1s

vertical distance travelled = 0.5*g*t^2 = 0.5*9.8*1 = 4.9 m

height remaining = 19.6 - 4.9 = 14.7 m

time required for 14.7m = ut +0.5gt^2 (here u = g*1 = 9.8 m/s after t = 1s)

so, 4.9t^2 + 9.8t - 14.7 = 0

t1 = 1s and t2 = -3 (time cannot be negative)

so the second has to travel in 1s to reach the ground along with the first one

so, 19.6 = u(1) + 0.5*9.8*1

u = 14.7 m/s (is the required initial velocity for the second one)