Physics problems: kinematics

Part 7


Problem 61.

A ball is thrown from a point 1 m above the ground.  The initial velocity is 20 m/s at an angle of 40 degrees above the horizontal.

(a) Find the maximum height of the ball above the ground.

(b) Calculate the speed of the ball at the highest point in the trajectory.



Problem 62.

A tortoise can run with a speed of 10.0 cm/s, and a hare can run exactly 10 times as fast. In a race, they both start at the same time, but the hare stops to rest for 3.00 min. The tortoise wins by 10 cm.

(a) How long does the race take?

(b) What is the length of the race?



Problem 63.

Emily takes a trip, driving with a constant velocity of 90 km/h to the north except for a 30 min rest stop. If Emily's average velocity is 75 km/h to the north, how long does the trip take?



Problem 64.

To qualify for the finals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 2000 m. If a particular car covers the first half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event to qualify?



Problem 65.

A skier is accelerating down a 30 degree hill at .

(a) What is the vertical component of her acceleration?

(b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation is 300 m?





Problem 66.

You are trying to cross a river that flows due south with a strong current. You start out in you motorboat on the west bank desiring to reach the east bank directly across from your starting point. Which direction should head your motorboat? Dram a picture of the river, the banks, and your motorboat, and include the relevant velocity vectors. What information would you need in order to determine the actual direction you need to head?



Problem 67.

(a) One liter ( ) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the (roughly circular) oil slick. Assume the oil molecules have a diameter of .

(b) Recalculate for the Exxon Valdez oil spill (March 1989), in which 11 million gallons (42 million L) of crude oil coated Prince William Sound in Alaska.



Problem 68.

The acceleration of an object as a function of time is . Determine the

(a) velocity and

(b) the position of the object as a function of time

if it is located at x = 2 m and has a velocity of 3 m/s at time t = 0 s.



Problem 69.

An automobile traveling 90 km/h overtakes a 1.5-km-long train traveling in the same direction on a track parallel to the road. If the train's speed is 70 km/h,

(a) how long does it take the car to pass it, and

(b) how far will the car have traveled in the time?



Problem 70.

Two cannonballs, A and B, are fired from the ground with identical initial speeds, but with launch angle of cannonball A larger than the launch angle of cannonball B.

(a) Which cannonball reaches a higher elevation?

(b) Which cannonball stays longer in the air?

(c) Which cannonball travels farther?





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