With what speed and angle of impact does the stone land?

[mre00]

Please Help!

I have figured out most of the problems for this assingment, however, I am having trouble with these:

1) A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 21.0 m/s. The cliff is h = 21.0 m above a flat horizontal beach.

How long after being released does the stone strike the beach below the cliff?
I got this part. Answer: 2.0702

I need help with thses -

With what speed and angle of impact does the stone land?
??

2) A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 20.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.21 m/s2 for a distance of 60.0 m to the edge of the cliff, which is 40.0 m above the ocean.
(a) Find the car's position relative to the base of the cliff when the car lands in the ocean.

(b) Find the length of time the car is in the air.

3) A student decides to measure the muzzle velocity of a pellet shot from his gun. He points the gun horizontally. He places a target on a vertical wall a distance x away from the gun. The pellet hits the target a vertical distance y below the gun.
(a) Show that the position of the pellet when traveling through the air is given by y = Ax2, where A is a constant. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Express the constant A in terms of the initial velocity v and the free-fall acceleration g.

(c) If x = 3.30 m and y = 0.205 m, what is the initial speed of the pellet?

4) The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of Acme power roller skates, which provide a constant horizontal acceleration of 15 m/s2, as shown in Figure P3.73. The coyote starts off at rest 70 m from the edge of a cliff at the instant the roadrunner zips by in the direction of the cliff.

(a) If the roadrunner moves with constant speed, find the minimum speed the roadrunner must have in order to reach the cliff before the coyote.

b) If the cliff is 100 m above the base of a canyon, find where the coyote lands in the canyon. (Assume that his skates are still in operation when he is in "flight" and that his horizontal component of acceleration remains constant at 15 m/s2.)

Please help me! I usually understand this stuff but had to miss a couple classes. This is due tomorrow morning.

 

[andrevdh]

1) Calculate the x and y velocity components. The speed is the magnitude of the resultant vector of these two. The angle can easily be calculated with the velocity components since they are perpendicular to each other. That is the resultant velocity and these two components form a right-angled triangle.

 

[andrevdh]

2) First calculate the launching speed of the car as it leaves the cliff.
(a) I think the intention is here that you use the parabolic equation to solve for x for the given y = 40.0 m
(b)This one is easy. If you are confident of your answer in (a) use the x-component of the launching velocity.

 

[andrevdh]

3) The parabolic equation is derived by eliminating time in the equation

$$y = v_{0y}t - 0.5gt^2$$

using

$$x = v_0 \cos(\theta _0) t$$