A stone projected upward from the top of a tower takes time t to reach its highest point and time 2t from the highest point to the ground. If its initial speed is u, the height of the tower is:
Options

Question

A stone projected upward from the top of a tower takes time t to reach its highest point and time 2t from the highest point to the ground. If its initial speed is u, the height of the tower is:

G1 Physics · Accepted Answer

Since time to the highest point is t, u=gt. Rise above the tower: upward rise = gt²/2 = u²/(2g). From the highest point to the ground, fall time is 2t: downward fall = (g/2)(2t)² = 2gt² = 2u²/g. Therefore tower height H = downward fall−upward rise = 2u²/g − u²/(2g) = 3u²/(2g).