A football is thrown with an initial upward velocity component of 15.0 m/s and a horizontal velocity component of 18.0 m/s
The time required for the football to reach the highest point in its trajectory is 1.53s.
It gets 11.5m above the ground.
How much time after it is thrown does it take to return to its original height?
How far has the football traveled horizontally from its original position?
To determine the time it takes for the football to return to its original height, we first need to find the total time of flight.
Given:
Initial upward velocity component (v_y) = 15.0 m/s
Horizontal velocity component (v_x) = 18.0 m/s
Time to reach highest point (t_max) = 1.53 s
The time of flight (t_flight) is twice the time to reach the highest point:
t_flight = 2 * t_max
t_flight = 2 * 1.53 s
t_flight = 3.06 s
Therefore, the time it takes for the football to return to its original height is 3.06 seconds.
To determine the horizontal distance traveled by the football, we can use the horizontal velocity component (v_x) and the time of flight (t_flight):
Horizontal distance (d) = v_x * t_flight
d = 18.0 m/s * 3.06 s
d = 55.08 m
Therefore, the football has traveled 55.08 meters horizontally from its original position.
To find out how much time it takes for the football to return to its original height after being thrown, we can analyze its vertical motion.
First, let's identify the key information given:
- Initial upward velocity component (v0y) = 15.0 m/s
- Time to reach the highest point (t) = 1.53 s
- Maximum height above the ground (h) = 11.5 m
To find the total time for the football to return to its original height, we can use the fact that the time taken to reach the maximum height is equal to the time taken to return to the original height.
Since the football will reach its highest point halfway through the total time (t/2), we can use this information to find the total time for the football to return to its original height.
Total time = 2 * (time to reach highest point)
= 2 * 1.53 s
= 3.06 s
Therefore, it will take 3.06 seconds for the football to return to its original height.
Moving on to the horizontal motion:
The horizontal velocity component (v0x) is given as 18.0 m/s. The distance traveled horizontally (d) can be calculated using the formula:
Distance = Horizontal velocity component * Time
Distance = 18.0 m/s * 3.06 s
= 55.08 m
Therefore, the football has traveled a horizontal distance of 55.08 meters from its original position.