Question
A placekicker kicks a football at initial speed of 22.2 m/s at an angle of 40.0°above the horizontal as shown in the figurer below.
Ignoring air resistance, calculate the total time the ball is in the air when it returns to its original height.
40y
I = Maximum height
a
"Ox
R = Range
00 s
14.3 s
17.0 s
2.92 s
1.46
Ignoring air resistance, calculate the total time the ball is in the air when it returns to its original height.
40y
I = Maximum height
a
"Ox
R = Range
00 s
14.3 s
17.0 s
2.92 s
1.46
Answers
GPT 3.5
s
To solve this problem, we need to break down the initial velocity into its horizontal and vertical components. The horizontal component of the initial velocity is given by Vx = 22.2 cos(40°) = 16.97 m/s and the vertical component is given by Vy = 22.2 sin(40°) = 14.31 m/s.
The time taken for the ball to reach its maximum height can be calculated using the formula for vertical motion: Vy = Voy - gt. At the maximum height, Vy = 0, so 0 = 14.31 - 9.8t. Solving for t gives t = 1.46 seconds.
Since the total time in the air is twice the time it takes to reach the maximum height, the total time in the air is 2 * 1.46 = 2.92 seconds. Therefore, the correct answer is 2.92 seconds.
To solve this problem, we need to break down the initial velocity into its horizontal and vertical components. The horizontal component of the initial velocity is given by Vx = 22.2 cos(40°) = 16.97 m/s and the vertical component is given by Vy = 22.2 sin(40°) = 14.31 m/s.
The time taken for the ball to reach its maximum height can be calculated using the formula for vertical motion: Vy = Voy - gt. At the maximum height, Vy = 0, so 0 = 14.31 - 9.8t. Solving for t gives t = 1.46 seconds.
Since the total time in the air is twice the time it takes to reach the maximum height, the total time in the air is 2 * 1.46 = 2.92 seconds. Therefore, the correct answer is 2.92 seconds.