Trouble Setting Up Projectile Motion

In summary, the problem involves a football being kicked at an angle of 53.0 deg. above horizontal with a speed of 20.0 m/s from a distance of 36.0 m away from the goal post. The crossbar is at a height of 3.05 m. The solution involves calculating the vectors Vnaught-x and Vnaught-y, with Vnaught-y representing the maximum height of the ball. The next step is to calculate the time at max height and evaluate the height of the ball at a distance of 36.0 m to determine if it will clear or fall short of the crossbar.
  • #1
quality101
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Problem: A football is kicked from 36.0 m away from goal post at an angle of 53.0 deg. above horizontal at a speed of 20.0 m/s. The crossbar is at a height of 3.05 m high. a.) By how far does the ball clear or fall short of the crossbar? b.) Does the ball approach the crossbar while still rising or while falling?

So far, I have drawn my sketch of the problem and I have chosen the x-y origin to be at the point the football is kicked, x being positive and height of crossbar (y) is positive.

I have also drawn out a vector right angle triangle to find the trigonometric relationship between Vnaught-x, Vnaught-y, and Vnaught. From the problem, Vnaught = 20.0 and theta = 53.0 deg. I now have solved Vnaught-x to be 12.04 and Vnaught-y to be 15.97. Is Vnaught-y the max height of the ball at a distance of 12.04 meters from the origin? If so, where do I go from here?

Thanks,
Steve
 
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  • #2
HUGE HINTS!
You might want to calculate the time at max height, so you can tell if the ball is falling or rising when it crosses the crosshair. Also consider evaluation Y when x= 36, so you can see how high will the ball be, and if it will be higher than 3.05 m.
 
  • #3


Hi Steve,

It seems like you have made a good start in setting up the problem. To answer your first question, Vnaught-y does represent the maximum height of the ball at a distance of 12.04 meters from the origin. To find the distance the ball clears or falls short of the crossbar, you will need to use the kinematic equations for projectile motion.

The first equation to use is the equation for the vertical displacement, which is y = y0 + v0y*t - 1/2*g*t^2. In this case, y0 (initial height) is 0 since the ball is kicked from ground level. v0y (initial vertical velocity) is 15.97 m/s and g (acceleration due to gravity) is -9.8 m/s^2. We are looking for the time (t) when the ball reaches a height of 3.05 m (height of the crossbar). So we can plug in these values and solve for t.

3.05 = 0 + (15.97)*t - 1/2*(-9.8)*t^2
3.05 = 15.97t + 4.9t^2
4.9t^2 + 15.97t - 3.05 = 0

Using the quadratic formula, we get two possible values for t: 0.15 s and -3.14 s. Since time cannot be negative, we can ignore the second solution. So the ball reaches a height of 3.05 m after 0.15 seconds. We can now use this time in the horizontal displacement equation, x = x0 + v0x*t, to find the horizontal distance the ball travels.

x = 0 + (12.04)*0.15
x = 1.81 meters

Since the ball was kicked from a distance of 36.0 m, we can see that it falls short of the crossbar by 36.0 - 1.81 = 34.19 meters.

To answer your second question, the ball approaches the crossbar while falling. This is because the vertical velocity decreases due to gravity, causing the ball to eventually fall back down to the ground.

I hope this helps you solve the problem. If you have any further questions, don't hesitate to ask. Good luck!
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air or space under the influence of gravity. It is a form of motion in which an object moves along a curved path due to its initial velocity and the constant force of gravity.

2. How do I calculate the initial velocity of a projectile?

The initial velocity of a projectile can be calculated using the formula v = √(gh), where v is the initial velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height from which the object is launched. Alternatively, it can also be calculated by using the horizontal and vertical components of the initial velocity.

3. What are the key factors that affect projectile motion?

The key factors that affect projectile motion are the initial velocity, the angle of launch, and the force of gravity. Other factors that can also affect it include air resistance, wind speed, and the shape of the object.

4. How do I set up a projectile motion experiment?

To set up a projectile motion experiment, you will need to gather the necessary materials such as a projectile object, a launcher, a protractor, and a ruler. Then, determine the initial velocity and angle of launch, and measure the distance traveled by the projectile. You can repeat the experiment with different initial velocities and angles to observe the effects on the projectile's motion.

5. What are some common challenges when setting up projectile motion experiments?

Some common challenges when setting up projectile motion experiments include ensuring accurate measurements, accounting for external factors such as air resistance and wind, and making sure that the object follows a parabolic path. It is also important to ensure that the launcher and the surface of launch are stable to obtain reliable results.

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