Question

Lacie kicks a football from ground level at a velocity of 13.9 m/s and at an angle of 25.0° to the ground. How long will the ball be in the air before it lands? How far will the football travel before it lands? How would this answer change if the football was kicked at a 35 degree angle?

Answer 1

Step-by-step explanation:

Given:

v₀ = 13.9 m/s

α₁ = 25.0°

α₂ = 35°

How long will the ball be in the air before it lands?

`\boxed{t=(2v_osin\alpha_1)/(g) }`

`t=(2(13.9)sin25^o)/(9.8)`

`=1.2\ s`

How far will the football travel before it lands?

`\boxed{x=(v_o^2sin(2\alpha))/(g) }`

`x=((13.9)^2sin(2*25^o))/(9.8)`

`=15.1\ m`

How would this answer change if the football was kicked at a 35 degree angle?

`t=(2(13.9)sin35^o)/(9.8)`

`=1.6\ s`

`x=((13.9)^2sin(2*35^o))/(9.8)`

`=18.5\ m`

Answer 2

The ball will be in the air for approximately 1.92 seconds and will travel approximately 26.66 meters before landing. If the ball was kicked at a 35-degree angle instead of a 25-degree angle, the time in the air will decrease and the horizontal distance traveled will increase.

Step-by-step explanation:

To find the time the ball will be in the air, we need to consider the vertical motion of the ball. The initial vertical velocity can be calculated by multiplying the initial velocity of the ball (13.9 m/s) by the sine of the launch angle (25.0°). Using this value, we can calculate the time it takes for the ball to hit the ground using the equation:

time = (2 * initial vertical velocity) / gravitational acceleration

Using the given values, we can calculate that the ball will be in the air for approximately 1.92 seconds.

To find the horizontal distance the ball will travel, we need to consider the horizontal motion of the ball. The horizontal velocity of the ball can be calculated by multiplying the initial velocity of the ball (13.9 m/s) by the cosine of the launch angle (25.0°). Using this value and the time calculated earlier, we can find the distance using the equation:

distance = horizontal velocity * time

Using the given values, we can calculate that the ball will travel approximately 26.66 meters before landing.

If the ball was kicked at a 35-degree angle instead of a 25-degree angle, the time it takes for the ball to hit the ground and the horizontal distance it travels will change. The time in the air will decrease, as a higher launch angle will result in a greater initial vertical velocity, causing the ball to hit the ground faster. The horizontal distance traveled will increase, as a higher launch angle will result in a greater horizontal velocity, causing the ball to travel a longer distance before landing.

Alternatively, you can use the equations of motion for projectile motion to calculate the time of flight and horizontal distance. The time of flight can be calculated using the formula:

time = (2 * initial vertical velocity) / gravitational acceleration * sin(launch angle)

And the horizontal distance can be calculated using the formula:

distance = initial horizontal velocity * time = initial velocity * cos(launch angle) * (2 * initial vertical velocity) / gravitational acceleration * sin(launch angle)