Question

question 21 (problem reference 3 - 3) a shell is fired with a horizontal velocity in the positive x direction from the top of an 80 - m high cliff. the shell strikes the ground 1330 m from the base of the cliff. the drawing is not to scale. determine the initial speed of the shell. a. 82 m/s b. 330 m/s c. 170 m/s d. 20 m/s

Explanation:

Step1: Calculate time of fall

Use vertical - motion equation $y = y_0+v_{0y}t+\frac{1}{2}at^{2}$. Here, $y = 0$, $y_0 = 80m$, $v_{0y}=0m/s$ and $a=-g=- 9.8m/s^{2}$. So, $0 = 80+0\times t-\frac{1}{2}\times9.8t^{2}$. Rearranging gives $4.9t^{2}=80$, then $t=\sqrt{\frac{80}{4.9}}\approx4.04s$.

Step2: Calculate initial horizontal speed

In horizontal direction, there is no acceleration ($a_x = 0$), and the horizontal - motion equation is $x = v_{0x}t$. We know $x = 1330m$ and $t\approx4.04s$. Then $v_{0x}=\frac{x}{t}=\frac{1330}{4.04}\approx330m/s$.

Answer:

B. 330 m/s