Concept explainers
A car is parked on a steep incline, making an angle of 37.0° below the horizontal and overlooking the ocean when its brakes fail and it begins to roll. Starting from rest at t = 0, the car rolls down the incline with a constant acceleration of 4.00 m/s2, traveling 50.0 m to the edge of a vertical cliff. The cliff is 30.0 m above the ocean. Find (a) the speed of the car when it reaches the edge of the dill, (b) the time interval elapsed when it at rives there. (c) the velocity of the car when it lands in the ocean, (d) the total time interval the cat is in motion, and (e) the position of the car when it lands in the ocean, relative to the base of the cliff.
(a)
The speed of car at the edge of cliff.
Answer to Problem 4.77AP
The speed of car at the edge of cliff is
Explanation of Solution
Given info: The angle of the incline is
The value of acceleration due to gravity is
The expression of kinematic equation of motion is,
Here,
Substitute
Conclusion:
Therefore the speed of car at the edge of the cliff is
(b)
The time taken by the car to reach the edge of cliff.
Answer to Problem 4.77AP
The time taken by the car to reach the edge of cliff is
Explanation of Solution
Given info: The angle of the incline is
The expression of kinematic equation of motion is,
Here,
Substitute
Conclusion:
Therefore the time taken by the car to reach the edge of cliff is
(c)
The velocity of the car when it lands in the ocean.
Answer to Problem 4.77AP
The velocity of the car when it lands in the ocean is
Explanation of Solution
Given info: The angle of the incline is
The expression for the horizontal component of velocity at the edge of the cliff,
Substitute
The horizontal component of velocity at the edge of the cliff is
There is no acceleration of car at the edge of cliff, thus the value of horizontal component of velocity does not change.
The expression for the vertical component of velocity at the edge of the cliff,
Substitute
The vertical component of velocity at the edge of the cliff is
The expression of kinematic equation of motion is.
Here,
Rearrange the above expression for value of
Substitute
The expression for the velocity of the car, when it lands on the ocean is,
Substitute
Conclusion:
Therefore, the velocity of the car when it lands in the ocean is
(d)
The total time interval of car in motion.
Answer to Problem 4.77AP
The total time interval of car in motion is
Explanation of Solution
Given info: The angle of the incline is
The expression for kinematics equation of motion is,
Here,
Rearrange the above equation for the value of
Substitute
The time period of fall of car is
The expression for the total time period of the motion of car is,
Substitute
Conclusion:
Therefore, the total time interval of car in motion is
(b)
The position of the car at the time it lands in the ocean relative to the base of the cliff.
Answer to Problem 4.77AP
The position of the car at the time it lands in the ocean relative to the base of the cliff is
Explanation of Solution
Given info: The angle of the incline is
The expression for horizontal distance travelled by the car during the fall from cliff is,
Substitute
The expression for position of car in vector form is,
Conclusion:
The position of the car at the time it lands in the ocean relative to the base of the cliff is
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