Im stuck ... my knowns are y_0= 1750 and x_f = about 350... i tried to get time
ID: 2006330 • Letter: I
Question
Im stuck ... my knowns are y_0= 1750 and x_f = about 350... i tried to get time by using height = 1/2 gt^2... but it seems like there is an initial velocity of the slide that i need to find time if im going to use y_f = y_o + v_i(t) -1/2(g) t^2 to find time.. or if im going about it the wrong way let me know..thanks
At 6:52 pm PDT Wednesday, July 10, 1996, a large block of granite with an estimated volume of 78,000 cubic yards detached from the cliff between Washburn Point and Glacier Point in Yosemite Valley. The estimated mass of the granite is 80,000 metric tons. Rock falls are a natural and continuous process on the granite cliffs in Yosemite Valley, however, most of the falls result in rock slides. This fall was unique in that it resulted in a projectile type of ballistic free-fall.
Shown on the last page is a profile of the fall. The rock mass slid down the rock shelf and went into the projectile motion seen in the diagram.
Use the profile and what you have learned about projectile motion to answer the following questions:
a. Use information about the rock shelf (see diagram) to determine the launch angle at the point where the rock mass went into projectile motion
b. Write the components of the rock’s velocity at the point where it went into projectile motion in terms of the initial launch angle and
c. Calculate the time the rock was in the air
d. Calculate the horizontal and vertical components of the rock’s velocity the instant before it struck the ground (final velocity components and )
e. Calculate the magnitude and direction (angle) of the final velocity
Explanation / Answer
Hi Anonymous, y_f = y_o + v_i(t) -1/2(g) t^2 is a result of finding the trajectory of object experiencing constant acceleration, however using the simplest kinematics(v=dx/dt, a=dv/dt) in this case wouldn't get you very far because of the unknown initial velocity and time. What I would do to solve the problem is to find the trajectory of the object first, and then by the trajectory solve for the velocity. Since the path is parabolic, you can find the trajectory by letting y=a*x^2+b*x+c, but what are the values of a,b and c? Find three points the object passes through, plug them in and solve for a,b and c. Once the trajectory is found, the problem becomes much simpler. First we can differentiate y to find the y component velocity: dy/dt=d(a*x^2+b*x+c)/dx * dx/dt = (2*a*x+b)*dx/dt differentiate y again to find y component acceleration: d(dy/dt)/dt=d((2*a*x+b)*dx/dt)/dt=2*a*(dx/dt)^2+(2*a*x+b)*d(dx/dt)/dt =2*a*(dx/dt)^2 But you know that the y-acceleration is -g, therefore dx/dt=(-g/(2a))^(1/2) Once you found dx/dt, you can then plug in dy/dt=(2*a*x+b)*dx/dt to find the initial y velocity (x=0). Once the initial velocity is found, I believe the problem should be very straight-forward for you, you can either use continue to use path coordinates or simply apply basic kinematics to solve the rest