One side of the roof of a building slopes up at 35.5°. A student throws a Frisbee onto the roof. It strikes with a speed of 15.0 m/s and does not bounce, but slides straight up the incline. The coefficient of kinetic friction between the plastic and the roof is 0.450. The Frisbee slides 10.0 m up the roof to its peak, where it goes into free-fall, following a parabolic trajectory with negligible air resistance. Determine the maximum height the Frisbee reaches above the point where it struck the roof.

thanks for the help!

To determine the maximum height the Frisbee reaches above the point where it struck the roof, we can use the principles of projectile motion and energy conservation.

Step 1: Calculate the initial vertical velocity
The Frisbee slides straight up the incline, therefore, we need to find the vertical component of its initial velocity.
Using trigonometry, we can find the vertical component:
Vertical velocity (V_y) = initial velocity (V) * sin(angle)
V_y = 15.0 m/s * sin(35.5°)

Step 2: Calculate the time the Frisbee takes to reach its peak
At the highest point, the vertical velocity becomes zero. The time taken to reach this point can be found using the equation:
V_y = V_0y + a * t
where V_y is the final vertical velocity (zero in this case), V_0y is the initial vertical velocity, a is the acceleration (which is due to gravity, -9.8 m/s^2), and t is the time.
0 = V_y + (-9.8 m/s^2) * t

Solve for t:
t = -(V_y / 9.8 m/s^2)

Step 3: Calculate the distance traveled horizontally
The horizontal distance traveled by the Frisbee can be calculated using the equation:
distance = speed * time
distance = 15.0 m/s * t

Step 4: Calculate the work done by friction while the Frisbee slides up the roof
The work done by friction can be calculated using the equation:
work = force * distance * cos(angle)
The force can be calculated using the equation:
force = coefficient of friction * mass * gravity
The mass cancels out when calculating the work done by friction.

Step 5: Calculate the initial vertical kinetic energy
The initial vertical kinetic energy can be calculated using the equation:
initial KE = 0.5 * mass * (initial velocity)^2

Step 6: Calculate the maximum height
The maximum height reached by the Frisbee can be found using the principle of energy conservation:
initial KE - work = final potential energy
final PE = mass * gravity * height

Rearrange the equation to solve for the maximum height:
height = (initial KE - work) / (mass * gravity)

Step 7: Substitute the known values and calculate the maximum height
Substitute the values into the equation and calculate the height:
height = (0.5 * mass * (initial velocity)^2 - force * distance * cos(angle)) / (mass * gravity)

Note: The mass of the Frisbee is not provided in the question. Make sure to substitute the appropriate value in the equation.

I hope this step-by-step guide helps you to solve the problem.

To determine the maximum height the Frisbee reaches above the point where it struck the roof, we need to break down the problem into different stages and solve each one separately. Let's go step by step:

Step 1: Find the acceleration of the Frisbee on the roof.
The force of kinetic friction is given by the equation:
F_k = μ * N
Where F_k is the force of kinetic friction, μ is the coefficient of kinetic friction, and N is the normal force.

The normal force can be calculated using the weight of the Frisbee, which is given by:
N = m * g
Where m is the mass of the Frisbee and g is the acceleration due to gravity (9.8 m/s^2).

Once we have the normal force, we can calculate the force of kinetic friction using the given coefficient of kinetic friction.

Step 2: Calculate the acceleration of the Frisbee on the roof.
We can use Newton's second law to determine the acceleration:
F_net = m * a
Where F_net is the net force acting on the Frisbee, m is its mass, and a is its acceleration.

The net force acting on the Frisbee is the force of kinetic friction. So, we can set up the equation:
F_k = m * a

Step 3: Determine the time it takes for the Frisbee to reach the peak.
Using the initial velocity (15.0 m/s) and the acceleration on the roof (from step 2), we can use the equation of motion:
v = u + a * t
Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

We know the final velocity is 0 m/s at the peak (since the Frisbee comes to a stop). So, we can rearrange the equation and solve for time.

Step 4: Find the distance traveled on the roof.
We can use the equation of motion to find the distance:
s = u * t + (1/2) * a * t^2
Where s is the distance traveled, u is the initial velocity, t is the time taken, and a is the acceleration.

We know the initial velocity is 15.0 m/s (given) and the acceleration is the one we calculated earlier in step 2. Rearrange the equation and solve for s.

Step 5: Determine the maximum height reached above the point where it struck the roof.
Using the distance traveled on the roof (from step 4) and the angle of the roof (35.5°), we can calculate the vertical displacement using trigonometry.

The vertical displacement can be calculated as:
h = s * sin(θ)
Where h is the maximum height reached, s is the distance traveled on the roof, and θ is the angle of the roof.

Plug in the values and solve for h.

By following these steps, you should be able to determine the maximum height the Frisbee reaches above the point where it struck the roof.

Well, I am not going to do it for you but will give some thoughts.

Approach it with energy reasoning.

The frisbee had kinetic energy when it hit the roof, (1/2) m v^2

It lost kinetic energy to potential climbing m g (10 sin 35.5)

It lost kinetic energy due to work done against friction
10 * .45 m g cos 35.5
subtract those two losses from initial Ke
That gives you the speed it departs the roof from Ke remaining =(1/2) m Vi^2
Now you have an ordinary projectile problem
departs the roof with vertical speed Vi sin 35.5
0 = Vi sin 35.5 - t 0
solve for t
H = 0 + Vi sin 35.5 t - 4.9 t^2