) 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)
The most useful kinematic equation for finding the ball's initial velocity in this scenario would be:
v = u + at
where:
v = final velocity of the ball (−3.5 m/s)
u = initial velocity of the ball (what we're trying to find)
a = acceleration (-9.8 m/s^2, due to gravity)
t = time taken (3 seconds)
To find the ball's initial velocity, we can use the following kinematic equation:
Final velocity (Vf) = Initial velocity (Vi) + (Acceleration x Time)
In this case, the final velocity is given as -3.5 m/s, the acceleration is -9.8 m/s^2 (negative because it is acting against the motion), and the time is 3 seconds.
Therefore, the most useful kinematic equation for finding the ball's initial velocity is:
Vf = Vi + (a * t)
To find the ball's initial velocity, we need to use a kinematic equation that relates the final velocity, initial velocity, acceleration, and time. In this case, the ball is rolling horizontally, which means the initial velocity and final velocity in the vertical direction are zero. Therefore, we can use the following kinematic equation:
v_f = v_i + a*t
Where:
v_f is the final velocity (-3.5 m/s),
v_i is the initial velocity (what we want to find),
a is the acceleration (-9.8 m/s^2),
and t is the time (3 seconds).
To find v_i, we rearrange the equation:
v_i = v_f - a*t
Substituting the given values:
v_i = -3.5 m/s - (-9.8 m/s^2) * 3 s
Simplifying:
v_i = -3.5 m/s + 29.4 m/s
v_i = 25.9 m/s
Therefore, the initial velocity of the ball is 25.9 m/s.
The most useful kinematic equation to find the ball's initial velocity in this case is v_i = v_f - a*t.