Ball on ramp and Merry Go Round problem

[john8910]

1) A small ball rolls down the frictionless ramp on the left (shown below). The angle of the
ramp is approximately 23 degrees, as shown, so the acceleration of an object rolling
down the ramp is g sin(23 deg) = 4 m/s^2.

The ball is given a push when it starts 1 meter away from the bottom of the ramp, so
initially it’s rolling downward with a velocity of 1 m/s.

Once the ball reaches the bottom of the ramp on the left, it starts rolling up the ramp on the right.

a) How much time does it take to reach the bottom of the ramp on the left?
(b) How fast is it going when it reaches the bottom of the ramp on the left?
(c) How far up the second ramp does the ball roll?
(d) How much time does it take to travel from the bottom of the ramp to the top of the
ramp on the right?


knowns:
Θ = 23, a = 4 m/s^2, xi= 0m, xf = 1m, vi = 1 m/s

i wasnt sure how to get a, so i started on b first, then i got a, but i don't know if this is the correct way to do it.
b)i used Vf^2 = Vi^2 + 2ax, and i got 9 m/s for final velocity
a) d = ((vi+vf)/2)*t, and i got 0.5s
c) I am sure on this one but i think i use vf^2 = Vi^2 + 2ax, and i got approx. 10 m
d) df = di+vit + 1/2at^2

practically, I am not sure how to start on a, and i need help on c and d.






2) I’m standing on the edge of a Merry-Go-Round that’s rotating around. I’m holding a ball in my hand. I toss it straight up in the air (in my reference frame).

When I toss the ball up in the air, the vertical component of the ball’s velocity is 5 meters per second. I’m 3 meters away from the center of the Merry-Go-Round, and it takes 6 seconds for the Merry-Go-Round to travel in a circle. It’s traveling clockwise.

(a) If the ball is 1 meter above the ground when tossed upward, how much time does the ball spend in the air before hitting the ground?
(b) How far away from my starting point does the ball land?
(c) What are all of the components of the ball’s velocity when it hits the ground?
Assume that the direction out of the page is the z direction

vi = 5m/s, r = 3 m ..

a) I am guessing y0= 0m, y1= 1m, vi = 5m/s, vf = 0m/s, a = -9.8 m/s2
i have trouble when the initial vi is not 0, i know i have to use xf=xi+vit+1/2at2
but I am not sure how to get t by itself.
b and c I am lost...

 

[Doc Al]

1)...

i wasnt sure how to get a, so i started on b first, then i got a, but i don't know if this is the correct way to do it.
b)i used Vf^2 = Vi^2 + 2ax, and i got 9 m/s for final velocity
a) d = ((vi+vf)/2)*t, and i got 0.5s
c) I am sure on this one but i think i use vf^2 = Vi^2 + 2ax, and i got approx. 10 m
d) df = di+vit + 1/2at^2

practically, I am not sure how to start on a, and i need help on c and d.

To solve a first, you can use the same formula that you have listed for d. (But it's perfectly OK to solve then in any order--there are several ways to attack this problem.)

Redo your calculation for b; looks like you forgot to take the square root.

Also, use a more accurate calculation for the acceleration. (Only round off at the end.)

2)...

a) I am guessing y0= 0m, y1= 1m, vi = 5m/s, vf = 0m/s, a = -9.8 m/s2
i have trouble when the initial vi is not 0, i know i have to use xf=xi+vit+1/2at2
but I am not sure how to get t by itself.
b and c I am lost...

That formula will give you a quadratic equation, which you can solve. xi = 1; xf = 0.