A football is kicked at 15 m/s with an angle of 35 degrees with the ground.

Question

A football is kicked at 15 m/s with an angle of 35 degrees with the ground.

How long is it in the air?
How far will it land?

Can someone help plz... Thanks!

Answer 1

The horizintal distance travelled t seconds following the kick is

X = 15 cos 35 * t
The vertical height is
Y = 15 sin 35 * t - (g/2) t^2

g = 9.8 m/s^2 is the acceleration of gravity

You should be familiar with these formulas.

Solve the Y equation for the time T when Y = 0. That will tell you how long the ball is in the air. Then use the X equation to find out how far it has travelled during that time T.

Answer 2

To find the time the football is in the air, we can use the vertical motion equation:

𝑦 = 𝑦₀ + 𝑣₀𝑡 − ½𝑔𝑡²

Where:
𝑦 is the vertical position at time 𝑡
𝑦₀ is the initial vertical position (which is 0 in this case)
𝑣₀ is the initial vertical velocity (which is the vertical component of the initial velocity of the football, given as 15 m/s * sin(35°))
𝑔 is the acceleration due to gravity, approximately 9.8 m/s²
𝑡 is the time in seconds

By substituting the given values into the equation, we can solve for 𝑡:

0 = 0 + (15 m/s * sin(35°))𝑡 − ½(9.8 m/s²)𝑡²

We can rearrange the equation to find 𝑡:

4.9𝑡² − (15 m/s * sin(35°))𝑡 = 0

Using the quadratic formula, 𝑡 = [−𝑏 ± sqrt(𝑏² − 4𝑎𝑐)] / 2𝑎, where 𝑎 = 4.9, 𝑏 = −(15 m/s * sin(35°)), and 𝑐 = 0, we can solve for 𝑡:

𝑡 = [−(−(15 m/s * sin(35°))) ± sqrt((−(15 m/s * sin(35°)))² − 4 * 4.9 * 0)] / (2 * 4.9)

Simplifying this expression will give you two possible values of 𝑡. We need to choose the positive one since time cannot be negative. This will represent how long the ball is in the air.

To find how far the ball will land, we can use the horizontal motion equation:

𝑥 = 𝑥₀ + 𝑣₀𝑥 * 𝑡

Where:
𝑥 is the horizontal distance traveled
𝑥₀ is the initial horizontal position (which is 0 in this case)
𝑣₀𝑥 is the initial horizontal velocity (which is the horizontal component of the initial velocity of the football, given as 15 m/s * cos(35°))
𝑡 is the time in seconds (which we found earlier)

Substituting the given values into the equation, we can solve for 𝑥:

𝑥 = 0 + (15 m/s * cos(35°)) * 𝑡

After obtaining the value of 𝑡 earlier, substituting it into the equation will give you the horizontal distance the ball will travel before landing.

Remember to convert the angles to radians if your calculator uses radians instead of degrees.