Question

A punter kicks a football at an angle of 32 degrees to the ground. The football has an initial velocity of 8.5 m/s. Assume g = 9.8 m/s2

a. How long does the football remain in the air?

b. How high will be ball go?

Answer 1

• 0.92s
• 1.95m

Step-by-step explanation:

To find:-

• Time during which football remains in air.
• Maximum height attained by the football.

Answer:-

Given that a punter kicks a football at 32° with a initial velocity of 8.5m/s.

When a ball is projected with initial velocity
`u` at an angle
`\theta` , then

Maximum height is given as;

`\longrightarrow\boxed{\rm Max^m \ height \ = \ (u^2\sin\theta)/(2g) }`

Time of flight is given as;

`\longrightarrow\boxed{\rm Time \ of \ flight\ = \ (2u\sin\theta)/(g) }`

Where,

• 
  `u` is the velocity of projection .
• 
  `\theta` is the angle of projection .

`\rule{200}2`

Part A :-

To find the time of flight we can substitute the respective values, in the above mentioned formula as;

`\longrightarrow \rm T_f = (2* 8.5\ m/s \ sin 32^\circ )/(9.8\ m/s^2) \\\\`

`\longrightarrow \rm T_f = ( 17* 0.53)/(9.8) s\\\\`

`\longrightarrow \rm \underline{\boxed{\rm\red{ Time \ of \ flight\ = 0.92 \ s }} }\\\\`

`\rule{200}2`

Part B :-

To find the maximum height we can substitute the respective values in the above mentioned formula as;

`\longrightarrow \rm H_(max) = ( (8.5\ m/s)^2 sin 32^\circ)/(2* 9.8\ m/s^2) \\\\`

`\longrightarrow \rm H_(max) = ( 72.25 * 0.53)/(19.6) m \\\\`

`\longrightarrow \underline{\boxed{\red{ \rm Max^m \ height = 1.95\ m }}}\\\\`

`\rule{200}2`

Hence the maximum height attained is 1.95m and the time of flight is 0.92s.

Answer 2

To find the time the ball remains in air, we can use the vertical motion equation and the given initial velocity and acceleration due to gravity. The horizontal distance can be found using the horizontal motion equation. The maximum height can be calculated using the equation for vertical distance traveled during half of the total time of flight.

Step-by-step explanation:

To find the answers for each part of the question, we can use the principles of projectile motion. Let's start with part (a), which asks how long the football remains in the air. We can use the vertical motion equation:

$$d = v_i t + rac{1}{2} g t^2$$

Since the initial vertical velocity is given as 8.5 m/s and the acceleration due to gravity is 9.8 m/s^2, we can plug in the values and solve for t. For part (b), we can use the horizontal motion equation:

$$d = v_i t$$

Substituting in the known values for the horizontal velocity and time, we can find the horizontal distance. Using the fact that the maximum height occurs halfway through the total time of flight, we can find the vertical distance traveled during that time. Therefore, the maximum height can be calculated using the equation:

$$d = v_{iy} t + rac{1}{2} g t^2$$

By plugging in the known values, we can find the maximum height of the ball.