A ball is rolled horizontally off the top of a table. After 3 seconds the ball lands on the ground with a final velocity of −3.5 m/s. Which kinematic equation would be most useful for finding the ball’s initial velocity? (Assume a= −9.8 m/s2)
V=V_0+a(delta)t
(delta)x=(v+v_0/2)(delta)t
(delta)x=v_0(delta)t+1/2 a((delta)t)^2
v^2=v_0^2+2a(delta)x
(delta)x=v(delta)t01/2a((delta)t)^2
The kinematic equation that would be most useful for finding the ball's initial velocity is:
(delta)x = v₀(delta)t + 1/2a((delta)t)^2
The most useful kinematic equation for finding the ball's initial velocity would be:
(delta)x = v_0(delta)t + 1/2 a((delta)t)^2
This equation relates the displacement (delta)x, initial velocity (v_0), acceleration (a), and time (delta)t. By rearranging the equation, you can solve for v_0.
To find the ball's initial velocity, we can use the kinematic equation:
(delta)x = v_0(delta)t + (1/2)a((delta)t)^2
In this equation, (delta)x represents the displacement (distance) traveled by the ball, v_0 represents the initial velocity, a represents the acceleration (gravity in this case), and (delta)t represents the time taken.
Given that the ball was in the air for 3 seconds (delta t = 3 s), and it landed with a final velocity of -3.5 m/s, we can substitute these values into the equation.
(-3.5 m/s) = v_0(3 s) + (1/2)(-9.8 m/s^2)((3 s)^2)
Now we can solve for v_0. Let's simplify the equation:
-3.5 m/s = 3v_0 - 44.1 m/s
Rearranging the equation, we get:
3v_0 = -3.5 m/s + 44.1 m/s
3v_0 = 40.6 m/s
Finally, isolating v_0, we divide both sides of the equation by 3:
v_0 = 40.6 m/s / 3
v_0 ≈ 13.53 m/s
So, the ball's initial velocity would be approximately 13.53 m/s.