Question

A projectile is fired from the top of a cliff of height h above the ocean below. The projectile is fired at an angle θ above the horizontal and with an initial speed vi.
(a) Find a symbolic expression in terms of the variables vi, g, and θ for the time at which the projectile reaches its maximum height.
t =

(b) Using the result of part (a), find an expression for the maximum height hmax above the ocean attained by the projectile in terms of h, vi, g, and θ.
hmax =

Answer 1

A projectile is fired from the top of a cliff of height $h$ above the ocean below. The projectile is fired at an angle $\theta$ above the horizontal and with an initial speed $vi$.

(a) Find a symbolic expression in terms of the variables $vi, g$, and $\theta$ for the time at which the projectile reaches its maximum height.

$$vi \cdot \sin \theta - g \cdot t = 0 \text{ when the projectile reaches its maximum height.}$$ $$t = \frac{vi \cdot \sin \theta}{g}$$

(b) Using the result of part (a), find an expression for the maximum height $h_{\max}$ above the ocean attained by the projectile in terms of $h$, $vi$, $g$, and $\theta$.

$$h_{\max} = h + vi \cdot \sin \theta \cdot t = h + \frac{vi^2 \cdot \sin^2 \theta}{g}$$