 University Physics Volume 1

79 .

A Formula One race car is traveling at 89.0 m/s along a straight track enters a turn on the race track with radius of curvature of 200.0 m. What centripetal acceleration must the car have to stay on the track?

80 .

A particle travels in a circular orbit of radius 10 m. Its speed is changing at a rate of $15.0m/s215.0m/s2$ at an instant when its speed is 40.0 m/s. What is the magnitude of the acceleration of the particle?

81 .

The driver of a car moving at 90.0 km/h presses down on the brake as the car enters a circular curve of radius 150.0 m. If the speed of the car is decreasing at a rate of 9.0 km/h each second, what is the magnitude of the acceleration of the car at the instant its speed is 60.0 km/h?

82 .

A race car entering the curved part of the track at the Daytona 500 drops its speed from 85.0 m/s to 80.0 m/s in 2.0 s. If the radius of the curved part of the track is 316.0 m, calculate the total acceleration of the race car at the beginning and ending of reduction of speed.

83 .

An elephant is located on Earth’s surface at a latitude $λ.λ.$ Calculate the centripetal acceleration of the elephant resulting from the rotation of Earth around its polar axis. Express your answer in terms of $λ,λ,$ the radius $RERE$ of Earth, and time T for one rotation of Earth. Compare your answer with g for $λ=40°.λ=40°.$ 84 .

A proton in a synchrotron is moving in a circle of radius 1 km and increasing its speed by $v(t)=c1+c2t2,wherec1=2.0×105m/s,v(t)=c1+c2t2,wherec1=2.0×105m/s,$
$c2=105m/s3.c2=105m/s3.$ (a) What is the proton’s total acceleration at t = 5.0 s? (b) At what time does the expression for the velocity become unphysical?

85 .

A propeller blade at rest starts to rotate from t = 0 s to t = 5.0 s with a tangential acceleration of the tip of the blade at $3.00m/s2.3.00m/s2.$ The tip of the blade is 1.5 m from the axis of rotation. At t = 5.0 s, what is the total acceleration of the tip of the blade?

86 .

A particle is executing circular motion with a constant angular frequency of $ω=4.00rad/s.ω=4.00rad/s.$ If time t = 0 corresponds to the position of the particle being located at y = 0 m and x = 5 m, (a) what is the position of the particle at t = 10 s? (b) What is its velocity at this time? (c) What is its acceleration?

87 .

A particle’s centripetal acceleration is $aC=4.0m/s2aC=4.0m/s2$ at t = 0 s where it is on the x-axis and moving counterclockwise in the xy plane. It is executing uniform circular motion about an axis at a distance of 5.0 m. What is its velocity at t = 10 s?

88 .

A rod 3.0 m in length is rotating at 2.0 rev/s about an axis at one end. Compare the centripetal accelerations at radii of (a) 1.0 m, (b) 2.0 m, and (c) 3.0 m.

89 .

A particle located initially at $(1.5j^+4.0k^)m(1.5j^+4.0k^)m$ undergoes a displacement of $(2.5i^+3.2j^−1.2k^)m.(2.5i^+3.2j^−1.2k^)m.$ What is the final position of the particle?

90 .

The position of a particle is given by $r→(t)=(50m/s)ti^−(4.9m/s2)t2j^.r→(t)=(50m/s)ti^−(4.9m/s2)t2j^.$ (a) What are the particle’s velocity and acceleration as functions of time? (b) What are the initial conditions to produce the motion?

91 .

A spaceship is traveling at a constant velocity of $v→(t)=250.0i^m/sv→(t)=250.0i^m/s$ when its rockets fire, giving it an acceleration of $a→(t)=(3.0i^+4.0k^)m/s2.a→(t)=(3.0i^+4.0k^)m/s2.$ What is its velocity $55$ s after the rockets fire?

92 .

A crossbow is aimed horizontally at a target 40 m away. The arrow hits 30 cm below the spot at which it was aimed. What is the initial velocity of the arrow?

93 .

A long jumper can jump a distance of 8.0 m when he takes off at an angle of $45°45°$ with respect to the horizontal. Assuming he can jump with the same initial speed at all angles, how much distance does he lose by taking off at $30°?30°?$

94 .

On planet Arcon, the maximum horizontal range of a projectile launched at 10 m/s is 20 m. What is the acceleration of gravity on this planet?

95 .

A mountain biker encounters a jump on a race course that sends him into the air at $60°60°$ to the horizontal. If he lands at a horizontal distance of 45.0 m and 20 m below his launch point, what is his initial speed?

96 .

Which has the greater centripetal acceleration, a car with a speed of 15.0 m/s along a circular track of radius 100.0 m or a car with a speed of 12.0 m/s along a circular track of radius 75.0 m?

97 .

A geosynchronous satellite orbits Earth at a distance of 42,250.0 km and has a period of 1 day. What is the centripetal acceleration of the satellite?

98 .

Two speedboats are traveling at the same speed relative to the water in opposite directions in a moving river. An observer on the riverbank sees the boats moving at 4.0 m/s and 5.0 m/s. (a) What is the speed of the boats relative to the river? (b) How fast is the river moving relative to the shore?

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