A place kicker must kick a football from a point 38.2 m from a goal. As a result of the kick, the ball must clear the crossbar, which is 3.05 m high. When kicked the ball leaves the ground with a speed of 20.6 m/s at an angle of 53° to the horizontal.

hi there budddddyy

Gtmyjbr

To determine whether the football clears the crossbar, we can analyze its projectile motion. Projectile motion is the motion of an object that is launched into the air and moves along a curved path under the influence of gravity.

To solve this problem, we'll use the following kinematic equations:

1. Horizontal displacement: x = v₀x * t
2. Vertical displacement: y = v₀y * t - (1/2) * g * t²
3. Velocity in the x-direction: vₓ = v₀x
4. Velocity in the y-direction: vᵧ = v₀y - g * t
5. Time of flight: t = 2 * v₀y / g

Where:
x and y are the x and y coordinates of the football at any given time t,
v₀x and v₀y are the initial velocities in the x and y directions, respectively,
g is the acceleration due to gravity (approximately 9.8 m/s²),
vₓ and vᵧ are the velocities in the x and y directions at any given time t.

First, we need to find the initial velocity components v₀x and v₀y using the given information.

Given:
Initial speed v₀ = 20.6 m/s
Launch angle θ = 53°

To find v₀x and v₀y:
v₀x = v₀ * cos(θ)
v₀y = v₀ * sin(θ)

Now, let's calculate v₀x and v₀y:
v₀x = 20.6 m/s * cos(53°) ≈ 11.16 m/s
v₀y = 20.6 m/s * sin(53°) ≈ 16.65 m/s

Next, we can determine the time of flight (t) using the equation:
t = 2 * v₀y / g

t = 2 * 16.65 m/s / 9.8 m/s² ≈ 3.39 s

Using the time of flight, we can calculate the horizontal displacement (x) using the equation:
x = v₀x * t

x = 11.16 m/s * 3.39 s ≈ 37.81 m

The horizontal displacement (37.81 m) is less than the required distance to the goal (38.2 m). Therefore, the ball will not clear the crossbar and the kick is unsuccessful.