Physics problems: kinematics

Part 4


Problem 31.

A missile is launched into the air at an initial velocity of 80 m/s. It is moving with constant velocity until it reaches 1000m, when the engine fails. 

(a) How long does it take it to reach 1000m?

(b) How high does the missile go?

(c) How long does it take for it to fall back to the earth? 

(d) How long does it stay in the air?

(e) How fast is it going when it hits the ground?



Problem 32.

The highest barrier that a projectile can clear is 14 m, when the projectile is launched at an angle of 30.0 degrees above the horizontal. What is the projectile's launch speed?



Problem 33.

A rocket is fired vertically upwards with initial velocity 80 m/s at the ground level. Its engines then fire and it is accelerated at until it reaches an altitude of 1000 m. At that point the engines fail and the rocket goes into free-fall. Disregard air resistance.

(a)  How long was the rocket above the ground?

(b)  What is the maximum altitude?

(c) What is the velocity just before it collides with the ground?



Problem 34.

An object is fired straight up at a speed of 9.8m/s. Compute its maximum altitude and the time it takes to reach that height. Ignore air resistance.



Problem 35.

A rock is dropped from rest into a well.

(a) The sound of the splash is heard 4 s after the rock is released from rest.

How far below to top of the well is the surface of the water? (the speed of sound in air at ambient temperature is 336m/s).

(b) If the travel time for the sound is neglected, what % error is introduced when the depth of the well is calculated?





Problem 36.

A ball is thrown upward with initial velocity v.  What is the change in speed on the way up? What is the change in speed on the way down? Disregard air resistance.



Problem 37.

A displacement, s, of an object as a function of time, t, is given by

a) Find an expression for the acceleration of the object

b) Explain why this expression indicates that the acceleration is not constant



Problem 38.

Snow is falling vertically at a constant speed of 3 m/s. At what angle from the vertical do the snowflakes appear to be falling as viewed by the driver of a car traveling on a straight, level road with a speed of 60 km/h?



Problem 39.

A dart is thrown horizontally with an initial speed of 10 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below P, 0.2 s later. What is the distance PQ? How far away from the dart board is the dart released?



Problem 40.

A boy walks to the store using the following path: 0.4 miles west, 0.2 miles north, 0.3 miles east.  What is his total displacement?  That is, what is the length and direction of the vector that points from her house directly to the store?





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