4.5 Relative Motion in One and Two Dimensions

A basketball player dribbling down the court usually keeps his eyes fixed on the players around him. He is moving fast. Why doesn’t he need to keep his eyes on the ball?

The coordinate axes of the reference frame $S^{'}$ remain parallel to those of $S$, as $S^{'}$ moves away from $S$ at a constant velocity $\overset{\rightarrow}{v}_{S^{'}}^{S} = \left(4.0 \hat{i} + 3.0 \hat{j} + 5.0 \hat{k}\right) \text{m} / \text{s} .$ (a) If at time t = 0 the origins coincide, what is the position of the origin $O^{'}$ in the S frame as a function of time? (b) How is particle position for $\overset{\rightarrow}{r} \left(t\right)$ and $\overset{\rightarrow}{r}^{'} \left(t\right) ,$ as measured in S and $S^{'} ,$ respectively, related? (c) What is the relationship between particle velocities $\overset{\rightarrow}{v} \left(t\right) \text{and} \overset{\rightarrow}{v}^{'} \left(t\right) ?$ (d) How…

The velocity of a particle in reference frame A is $\left(\right. 2.0 \hat{i} + 3.0 \hat{j} ) \text{m} / \text{s} .$ The velocity of reference frame A with respect to reference frame B is $4.0 \hat{k} \text{m} / \text{s} ,$ and the velocity of reference frame B with respect to C is $2.0 \hat{j} \text{m} / \text{s} .$ What is the velocity of the particle in reference frame C?

A seagull can fly at a velocity of 9.00 m/s in still air. (a) If it takes the bird 20.0 min to travel 6.00 km straight into an oncoming wind, what is the velocity of the wind? (b) If the bird turns around and flies with the wind, how long will it take the bird to return 6.00 km?

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?

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?

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 $3.00 \text{m} / \text{s}^{2} .$ 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?

A particle’s centripetal acceleration is $a_{\text{C}} = 4.0 \text{m} / \text{s}^{2}$ 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?

A particle located initially at $\left(1.5 \hat{j} + 4.0 \hat{k}\right) \text{m}$ undergoes a displacement of $\left(2.5 \hat{i} + 3.2 \hat{j} - 1.2 \hat{k}\right) \text{m} .$ What is the final position of the particle?

A spaceship is traveling at a constant velocity of $\overset{\rightarrow}{v} \left(t\right) = 250.0 \hat{i} \text{m} / \text{s}$ when its rockets fire, giving it an acceleration of $\overset{\rightarrow}{a} \left(t\right) = \left(3.0 \hat{i} + 4.0 \hat{k}\right) \text{m} / \text{s}^{2} .$ What is its velocity $5$ s after the rockets fire?

A long jumper can jump a distance of 8.0 m when he takes off at an angle of $45 °$ 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 $30 ° ?$

A mountain biker encounters a jump on a race course that sends him into the air at $60 °$ 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?

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?

World’s Longest Par 3. The tee of the world’s longest par 3 sits atop South Africa’s Hanglip Mountain at 400.0 m above the green and can only be reached by helicopter. The horizontal distance to the green is 359.0 m. Neglect air resistance and answer the following questions. (a) If a golfer launches a shot that is $40 °$ with respect to the horizontal, what initial velocity must she give the ball? (b)…

A truck is traveling east at 80 km/h. At an intersection 32 km ahead, a car is traveling north at 50 km/h. (a) How long after this moment will the vehicles be closest to each other? (b) How far apart will they be at that point?