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What is the sign of the accelerations of the cart (in the x direction) the instant it reaches its turn around point at the maximum height?

What is the sign of the accelerations of the cart (in the x direction) the instant it reaches its turn around point at the maximum height?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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What is the sign of the accelerations of the cart (in the x direction) the instant it reaches its turn around point at the maximum height?

a. Positive 

b. Negative 

c. Zero

**Questions:** The first two questions are about the following situation: Suppose that a low-friction cart is placed on a tilted track (see picture below). The cart is given an initial shove up the incline, in the positive x-direction. The cart is observed to slow down, reach a maximum height, and then turn around and speed up back down the incline. Treat the cart as a point object, with its position measured at its center. Note that this diagram is a sketch and the tilt of the ramp is exaggerated. **Diagram Description:** The diagram illustrates a cart on an inclined track. The track is tilted and extends from the left, marked with a positive x-direction (+x). The initial position of the cart is marked at \( x = 0 \) with an initial velocity of \( v_i = 5 \, \text{m/s} \) going up the incline. A point further up the incline is marked \( x = 4 \, \text{m} \), which is labeled as the "turn around point," indicating the maximum height reached by the cart before it reverses direction.
Transcribed Image Text:**Questions:** The first two questions are about the following situation: Suppose that a low-friction cart is placed on a tilted track (see picture below). The cart is given an initial shove up the incline, in the positive x-direction. The cart is observed to slow down, reach a maximum height, and then turn around and speed up back down the incline. Treat the cart as a point object, with its position measured at its center. Note that this diagram is a sketch and the tilt of the ramp is exaggerated. **Diagram Description:** The diagram illustrates a cart on an inclined track. The track is tilted and extends from the left, marked with a positive x-direction (+x). The initial position of the cart is marked at \( x = 0 \) with an initial velocity of \( v_i = 5 \, \text{m/s} \) going up the incline. A point further up the incline is marked \( x = 4 \, \text{m} \), which is labeled as the "turn around point," indicating the maximum height reached by the cart before it reverses direction.
Expert Solution
Step 1

At maximum height vf  will be zero.

Given

s=4m

vi=5m/s

vf = 0m/s

Apply Equation of Motion

vf2-v2i=2as

s=-v2i/2s

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