A ball is thrown vertically upward with a speed of +12.0m/s.
A. how long the ball take to hit the ground after it reaches it highest point?
B. What is its velocity when it returns to the level from with it started?
A tortoise can run with a speed of 0.12m/s and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell(25cm).
A. how long does the race takes?
B. What is the length of race?
Please post one question at a time.
The speed when the ball hits the ground will again be 12 m/s (because of conservation of energy), but the direction will be reversed, making it -12.0 m/s.
The time of flight AFTER reaching max height will be the time it takes to accelerate to a speed of 12 m/s, which is 12/g = 12/9.8 s.
A tortoise can run with a speed of 13.0 cm/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 5.0 minutes. The tortoise wins by a shell (40 cm).
(a) How long does the race take?
s
(b) What is the length of the race?
m
To solve both parts of the question, we can use the formulas of motion for vertical motion under constant acceleration.
A. To determine how long it takes for the ball to hit the ground after reaching its highest point, we can use the fact that at the highest point of its trajectory, the ball's vertical velocity becomes zero. The acceleration acting on the ball is due to gravity, which is -9.8 m/s^2 (negative because it acts in the opposite direction to the initial velocity). We can use the formula:
v = u + at
Where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (+12.0 m/s)
a = acceleration due to gravity (-9.8 m/s^2)
t = time taken
Rearranging the formula to solve for t:
t = (v - u) / a
Plugging in the values:
t = (0 - 12.0) / -9.8
t = 1.22 seconds
Therefore, it takes approximately 1.22 seconds for the ball to hit the ground after reaching its highest point.
B. To find the velocity of the ball when it returns to the level from which it started, we need to consider that the ball will have the same magnitude of velocity as its initial velocity but in the opposite direction. Therefore, the velocity will be -12.0 m/s.
Note: The negative sign indicates the direction is downward, opposite to the initial direction of throw.
So, the velocity of the ball when it returns to the level from which it started is -12.0 m/s.