Final answer:
The rocket takes approximately 4.59 seconds to reach its highest point, rises approximately 103.56 meters above the ground, and takes approximately 9.18 seconds to hit the ground again.
Step-by-step explanation:
a. How long does it take the rocket to reach its highest point?
To find the time it takes for the rocket to reach its highest point, we can use the equation:
time = (Final velocity - Initial velocity) / acceleration
Since the rocket shoots straight up, the final velocity at its highest point is 0 m/s. The initial velocity is 45.0 m/s and the acceleration is due to gravity, which is -9.8 m/s². Plugging these values into the equation:
time = (0 - 45.0) / (-9.8) = 4.59 seconds
So, it takes approximately 4.59 seconds for the rocket to reach its highest point.
b. How high does the rocket rise above the ground?
To find the height the rocket reaches, we can use the kinematic equation:
final velocity² = initial velocity² + 2 * acceleration * displacement
Since the final velocity is 0 m/s at the highest point, the equation becomes:
0 = 45.0² + 2 * (-9.8) * displacement
solving for displacement:
displacement = (45.0²) / (2 * 9.8) = 103.56 meters
So, the rocket rises approximately 103.56 meters above the ground.
c. How long does it take the rocket to hit the ground again?
The time it takes for the rocket to hit the ground again is equal to twice the time it took to reach its highest point (as the motion is symmetrical). Therefore, it takes approximately 2 * 4.59 = 9.18 seconds for the rocket to hit the ground again.