# Kinematics in Two dimensions – Problems

Mechanics

Nov 14, 2013 (4 years and 6 months ago)

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Projectiles&2DmotionProbs.AP
Name____________________Date_______

Kinematics in Two dimensions

Problems

Warm
-
up Problems

1.

A radar antenna is tracking a satellite orbiting the earth. At a certain time, the radar
screen shows the satellite to be 162km away. The radar antenna is pointing upward at an
angle of 62.3
0

from the ground Find the x and y components (in km) of the position of the
satellite.

2.

Divers at Acapulco dive from a cliff that is 40m high. If the rocks below the cliff extend
outward for 13m, what is the minimum horizontal velocity (v
x
) a diver

must have to clear
the rocks safely?

3.

A projectile is launched at an angle of 30
0

above horizontal with an initial speed of
20m/s.

a.

How much time is it in the air?

b.

What is the highest point in its trajectory?

c.

What is its horizontal
range

(

x)?

Projectiles&2DmotionProbs.AP
Name____________________Date_______

Displacement, velocity and acceleration

4.

A jetliner is moving at a speed of 245 m/s. The vertical component of the plane’s velocity is 40.6
m/s. Determine the magnitude of the horizontal component of the plane’s velocity.

5.

In a football game a kicker attempts a field goal. The ball remains in contact with the kicker’s foot
for 0.050s, during which time it experiences an acceleration of 340 m/s
2
. The ball is launched at
an angle of 51
0

above the ground. Determine the horiz
ontal and vertical components of the launch
velocity.

6.

The earth moves around the sun in a nearly circular orbit of radius 1.50X10
11
m. During the three
summer months (an elapsed time of 7.89X10
6
s), the earth moves one
-
fourth of the distance around

the sun.

a.

What is the average speed of the earth?

b.

What is the magnitude of the average velocity of the earth during this period?

Projectiles&2DmotionProbs.AP
Name____________________Date_______

Equations of kinematics in two dimensions

7.

On a spacecraft, two eng
ines are turned on for

684 s at a moment when the velocity of the craft
has x and y components of v
ox
=4370m/s and v
oy

=6280m/s. While the engines are firing, the craft
undergoes a displacement that has components of x=4.11X10
6
m and y=6.07X10
6
m. Find the x
and y components of
the craft’s acceleration.

Projectile Motion

8.

A daredevil is shot out of a cannon at 18m/s at an angle of 30
0
above horizontal. A net is placed
20m away from the daredevil and safely catches him.

a.

How long is the daredevil in the air?

b.

How

high is the net above the daredevil’s original position?

9.

A baseball leaves a bat with a velocity of 35m/s at an angle of 32
0

above horizontal.

a.

What is the highest point in its path?

b.

When will it strike a billboard in center field 8.0m
above the field?

Projectiles&2DmotionProbs.AP
Name____________________Date_______

10.

Suppose the water at the top of Niagara Falls has a horizontal speed of 2.7m/s just before it
cascades over the edge of the falls. At what vertical distance below the edge does the velocity
vector of the water point downward at a 7
5
0

angle below the horizontal?

11.

An Olympic long jumper leaves the ground at an angle of 23
0

and travels through the air for a
horizontal distance of 8.7m before landing. What is the takeoff speed of the jumper?

12. The drawing shows and exaggerated view of a rifle that has “sighted in” for a 91.4m target. If the
muzzle speed of the bullet is v
o
=427m/s, what are the two possible angles

1

and

2

between the rifle
barrel and the horizontal such that the bullet w
ill hit the target.
(Hint: the following trig identity may be
useful: 2sin

cos

= sin2

)