3.)
If a ball that is 4 meters above the ground is thrown horizontally at 4 meters per second, how long will it take for the ball to hit the ground?
In this problem, it’s important to note that the kinematic equations should be used to account for
motion in one direction only (either in the horizontal or vertical direction). As such, the initial velocity of
the ball is zero because we are only concerned with finding the time it take the ball to travel 4 meters
vertically. It may be helpful to use subscripts when applying the equations, as shown below.
=
+
+
1
2
In this case, the initial velocity of the ball in the y-direction (v
0y
) is zero and the acceleration in the y-
direction (a
y
) is equal to gravity.
If we look back at problem 2, this is actually a very similar problem! Once the ball reaches its peak in
problem 2, it also has zero initial velocity in the y-direction and the acceleration in the y-direction is
equal to gravity. Therefore, we can use the time it took in problem 2 for the ball to descend from its
peak to hit the ground (0.408 seconds) to solve this problem.
So our answer is 0.408 seconds.
4.) In question 3, how far will the ball travel in the horizontal direction before it hits the ground?
To solve this problem, either Equation 2 or 4 can be applied by using the time found in Question 3. For
equation 2, the initial location of the ball (x
0
) is zero as is the acceleration of the ball in the x-direction
(a
x
=
+
+
1
2
= 0 + 4
(
0.903
)
+
1
2
0
(
0.903
)
= 3.61
Using Equation 4, it can be assumed that the final velocity of the ball in the x-direction is the same as the
initial velocity in the x
-dire
ction (when air resistance is neglected, a r
easonable assumption). Solving for