Well it's an kinematics project and it involves alot of questions. So here goes the problem:
Suppose a football was thrown at an angle of 37 degrees with a velocity of 90mi/hr while leaving a quarterback hand at a height of 6'4" above the ground. A)Calculate the maximum height of the football after being thrown. B)Find the velocity vector at the maximum height. C) find the acceleration vector at the maximum height D) calculate the time traveled before the ball was caught at the height it waas thrown. E)How far did the ball travel before being caught F) calculate the force needed for a 185lb receiver to leap and catch the ball at the height it was thrown hint:the tme it took the receiver to accelerate from the ground was 0.25seconds. G) calculate the impulse experienced when the receiver landed firmly on the ground after catching the ball H) estimate the average force exerted on the person's feet by the ground after landing stiff legged, assume the body moved 1.0cm during impact. After catching the ball and landing onto the field the receiver is immediately tackled by a 150lb strong safety with an initial velocity of 25mi/hr. I) Calculate the final velocity of the two colliding masses J) Calculate how much of the strong safety initial kinetic energy is transformed to thermal or other forms of energy after the collision.
To solve this kinematics project, we will go step by step and use the equations of motion to find the required quantities.
A) Calculate the maximum height of the football after being thrown:
To find the maximum height, we need to determine the vertical component of the initial velocity. Given that the football was thrown at an angle of 37 degrees with a velocity of 90 mi/hr, we can first find the vertical component using trigonometry:
Vertical component = Initial velocity * sin(angle)
= 90 mi/hr * sin(37 degrees)
Now, convert the vertical component from mi/hr to ft/s (since the height is given in feet):
Vertical component = 90 mi/hr * (5280 ft/1 mi) * (1 hr/3600 s) * sin(37 degrees)
The vertical component of velocity gives us the rate of change of height with respect to time. We can use this information to find the time it takes for the football to reach maximum height. The formula to find time is:
Time = Vertical component / (Acceleration due to gravity)
= Vertical component / (32.2 ft/s^2)
Next, we can find the maximum height using the following kinematic equation:
Maximum height = Initial height + (Vertical component)^2 / (2 * Acceleration due to gravity)
Substitute the values we have, and the maximum height can be calculated.
B) Find the velocity vector at the maximum height:
The velocity vector at the maximum height will have the same magnitude as the initial velocity but in the opposite direction. However, the direction can be determined using the angle of projection (37 degrees in this case).
C) Find the acceleration vector at the maximum height:
The acceleration vector at the maximum height will be directed towards the ground and have a magnitude equal to the acceleration due to gravity (32.2 ft/s^2).
D) Calculate the time traveled before the ball was caught at the height it was thrown:
To find the time traveled before the ball was caught, we need to consider both the vertical and horizontal components of motion. Since the vertical motion is affected by gravity, we already have the time it took for the ball to reach maximum height from part A. To find the total time of flight, we need to double the time it took to reach maximum height.
Total time of flight = 2 * Time
E) How far did the ball travel before being caught:
To find the horizontal distance covered by the ball before being caught, we can use the horizontal component of the initial velocity and the total time of flight. The formula is:
Horizontal distance = Horizontal component * Total time of flight
F) Calculate the force needed for a 185 lb receiver to leap and catch the ball at the height it was thrown:
To calculate the force needed, we need to consider the work-energy principle. The work done on the receiver is equal to the change in kinetic energy. We can use the relationship between work and force to find the force exerted.
Force = Work done / Distance
First, determine the work done using the equation:
Work done = Change in kinetic energy
The change in kinetic energy is the difference between the final kinetic energy (when the receiver caught the ball) and the initial kinetic energy (when the receiver leaves the ground). Finally, divide the work done by the distance to find the force needed.
G) Calculate the impulse experienced when the receiver landed firmly on the ground after catching the ball:
Impulse is defined as the change in momentum. To calculate impulse, we'll need the initial and final velocities and the mass of the receiver. We can use the equation:
Impulse = Mass * (Final velocity - Initial velocity)
H) Estimate the average force exerted on the person's feet by the ground after landing stiff legged, assuming the body moved 1.0 cm during impact:
To estimate the average force exerted on the person's feet, we can first calculate the change in momentum during impact. The change in momentum is the product of mass and the change in velocity. Since the time of impact is not provided, we'll assume it's very short (instantaneous).
Once we have the change in momentum, we can calculate the average force using the equation:
Average force = Change in momentum / Time of impact
I) Calculate the final velocity of the two colliding masses:
To calculate the final velocity of the two masses (the receiver and the strong safety), we can use the law of conservation of momentum. Since this is a one-dimensional collision, the equation is:
Total initial momentum = Total final momentum
Momentum is the product of mass and velocity, so the equation can be rewritten as:
(mass of receiver * initial velocity of receiver) + (mass of strong safety * initial velocity of strong safety) = (mass of receiver * final velocity of receiver) + (mass of strong safety * final velocity of strong safety)
Rearrange the equation to solve for the final velocity of the two masses.
J) Calculate how much of the strong safety's initial kinetic energy is transformed to thermal or other forms of energy after the collision:
To calculate the amount of initial kinetic energy transformed to other forms, we need to subtract the final kinetic energy from the initial kinetic energy for the strong safety. Kinetic energy is given by the formula:
Kinetic energy = 0.5 * mass * velocity^2
Calculate the initial kinetic energy for the strong safety and subtract the final kinetic energy after the collision to find how much energy is transformed.