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Find the angle between the two vectors

A = 2i + 3j + k and B= -4i + 2j –k

Find the total displacement.

2.51 The acceleration of a motorcycle is given by ax (t) = At – Bt2, where A = 1.5 m/s3 and B = 0.120 m/s4.

The motor-cycle is at rest at the origin at time t = 0.

(a) Find its position and velocity as functions of time.

(b) Calculate the maximum velocity it attains.

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A motorist traveling with a constant speed of 15 m/s passes a school-crossing corner, where the speed

limit is 10 m/s. Just as the motorist passes, a police officer on a motorcycle stopped at the corner starts

off in pursuit with constant acceleration of 3.0 m/s2.

(a)  How much time elapses before the officer catches up with the motorist?

(b)  What is the officer’s speed at that point?  

(c)  What is the total distance each vehicle has travelled at that point?

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A one-euro coin is dropped from the Leaning Tower of Pisa. It starts from rest and falls freely.

Compute its position and velocity after 1.0 s, 2.0 s, and 3.0 s.

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You throw a ball vertically upward form the roof of a tall building. The ball leaves your hand at a

point even with the roof railing with an upward speed of 1.50 m/s; the ball is then in free fall. On

its way back down, it just misses the railing. At the location of the building is g = 9.80 m/s2

.Find (a) the position and velocity of the ball 1.00 s and 4.00 s after leaving your hand; (b) the

velocity when the ball is 5.00 m above the railing; (c) the maximum height reached and the time

at which it is reached; and (d) the acceleration of the ball when it is at its maximum height.

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Find the time when the ball is 5.00 m below the roof railing.

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Sally is driving along a straight highway in her class 1965 Mustang. At time t = 0, when Sally is

moving at 10 m/s in the positive x -direction, she passes a signpost at x = 50 m. Her x-

acceleration is a function of time :

ax = 2.0 m/s2  – (0.10 m/s3 ) t

a.  Find her x-velocity and position as functions of time.

b.  When is her x-velocity greatest?

c.  What is the maximum x-velocity?

d. 

Where is the car when it reaches the maximum x-velocity?

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8/9/2019 PHY10 de Review Questions

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A robotic vehicle, or rover, is exploring the surface of mars. The landing craft is the origin of the

coordinates, and the surrounding Martian surface lies in the xy -plane. The rover, which we represent as

a point, has a x - and y-coordinates that vary with time:

X = 2.0 m – (0.25 m/s2)t2

Y = (1.0 m/s)t + (0.025 m/s3)t3

(a)  Find the rover’s coordinates and its distance from the lander at t = 2.0 s.  

(b)  Find the rover’s displacement and average velocity vectors during the interval from 

t = 0 s to t = 2.0s.

(c ) Derive a general expression for the rover’s instantaneous velocity vector. Express the

instantaneous velocity at t = 2.0s in component form and also in terms of magnitude and direction.

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A batter hits a baseball so that it leaves the bat at speed v0 = 37 m/s at an angle α0 = 53.1°, at a location

where g = 9.80 m/s2 .

(a)  Find the position of the ball, and the magnitude and direction of its velocity, at t=2.00 s.

(b)  Find the time when the ball reaches the highest point of its fl ight and find its height h at this

point.

(c)  Find the horizontal range R – that is, the horizontal distance from the starting point to where the

ball hits the ground.

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You toss a ball from your window 8.0 m above the ground. When the ball leaves your hand, it is moving

at 10.0 m/s at an angle of 20 ° below the horizontal. How far from your window wil l the ball hit the

ground? Ignore air resistance.