Sean kicks a soccer ball with an initial velocity of 70 ft/sec at an angle of 41° with the horizontal. Answer the following questions:How long is the ball in the air? Blank 1 Question 7How far does the ball travel horizontally?
Question
Sean kicks a soccer ball with an initial velocity of 70 ft/sec at an angle of 41° with the horizontal. Answer the following questions:How long is the ball in the air? Blank 1 Question 7How far does the ball travel horizontally?
Solution
To solve these problems, we need to use the equations of motion. We also need to break down the initial velocity into its horizontal and vertical components.
- How long is the ball in the air?
First, we need to find the initial vertical velocity. We can do this using the formula:
Viy = Vi * sin(θ)
where Vi is the initial velocity (70 ft/sec) and θ is the angle (41°).
Viy = 70 * sin(41°) = 45.64 ft/sec
The time the ball is in the air (also known as the time of flight) can be found using the formula:
t = 2 * Viy / g
where g is the acceleration due to gravity. In feet per second squared, g is approximately 32.2 ft/sec².
t = 2 * 45.64 / 32.2 = 2.83 seconds
So, the ball is in the air for approximately 2.83 seconds.
- How far does the ball travel horizontally?
First, we need to find the initial horizontal velocity. We can do this using the formula:
Vix = Vi * cos(θ)
Vix = 70 * cos(41°) = 53.13 ft/sec
The horizontal distance the ball travels (also known as the range) can be found using the formula:
d = Vix * t
d = 53.13 * 2.83 = 150.35 feet
So, the ball travels approximately 150.35 feet horizontally.
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