Final answer:
a) The maximum height is approximately 16.53 meters. b) The vertical component of velocity when it hits the ground is -18.0 m/s. c) The time taken to reach the ground is approximately 3.67 seconds. d) The range is 0 meters. e) The velocity of impact is -18.0 m/s.
Step-by-step explanation:
a) To calculate the maximum height, you can use the equation for vertical motion:
final velocity squared = initial velocity squared + 2 * acceleration * distance
Since the stone was thrown vertically upwards, the final velocity at maximum height is 0. So rearranging the equation, you get:
0 = (18.0 m/s)2 + 2 * (-9.8 m/s2) * distance
Solving for distance, the maximum height is approximately 16.53 meters.
b) The vertical component of velocity when the stone hits the ground is the same as when it was thrown upwards, but with the opposite sign. So the vertical component of velocity when it hits the ground is -18.0 m/s.
c) To calculate the time taken to reach the ground, you can use the equation:
time = (final velocity - initial velocity) / acceleration
Since the stone was thrown upwards and comes back down, the final velocity is -18.0 m/s, and the initial velocity is 18.0 m/s. The acceleration is -9.8 m/s2 because gravity is acting downwards. Plugging in the values, the time taken to reach the ground is approximately 3.67 seconds.
d) The range is the horizontal distance covered by the stone. Since the stone was thrown vertically upwards, the initial horizontal velocity is 0. Therefore, the range is also 0 meters.
e) The velocity of impact is the velocity with which the stone hits the ground. Since the stone was thrown upwards, the vertical component of the velocity when it hits the ground is -18.0 m/s, as calculated in part b. The horizontal component of the velocity remains 0, as explained in part d. Therefore, the velocity of impact is -18.0 m/s.