A rock is thrown horizontally from the top of a radio tower lands 17.0 m from the base of the tower. if the speed at which the object was projected was 9.50 m/s, how high is the tower?

For this problem, we use the equations derived from the projectile motion. Particularly, we use the trajectory of the projectile equation written below:

y = xtanθ + gx/2v₀²cosθ

where

y is the vertical height

x is the horizontal distance

θ is the launch angle

g is 9.81 m/s²

v₀ is the initial velocity

Since it was thrown horizontally, θ = 0°. Substituting the values,

y = 17tan0° + (9.81) (17) / 2 (9.50) ²cos0°

y = 0.924 m