Answer to Question #152392 in Calculus for Sarah Bittence

Question

the acceleration due to gravity on the planet Calcllceara is -10m/s^2. A stone is thrown downwards with a speed of 5 m/s from the upper observation deck of the Base Camp Alpha Tower, 150 m above the ground

Answer 1

Kinematic equations for objects thrown downwards

We assume here that acceleration equals $-a=-10 m/s^2$  (with the positive direction upward).

$$v=v_0+at$$

$$y=y_0+v_0t+\dfrac{at^2}{2}$$

$$v^2=v_0^2+2a(y-y_0)$$

Given $y_0=150m, v_0=-5m/s, a=-10m/s^2$

$$y_1=0:0=150-5t-\dfrac{10t^2}{2}$$

$$t^2+t-30=0$$

$$t_1=-6, t_2=5$$

Since $t\geq0,$ we take $t_2=5s.$

$$v(5)=-5-10(5)=-55(m/s)$$

The stone will fall down the ground after 5 seconds. Its velocity will be 55 m/s when it falls down the ground.