Question

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?

Answer 1

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