A student stands at the edge of a cliff and throws a stone horizontally over the

Question

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 12.0 m/s. The cliff is h = 29.0 m above a flat, horizontal beach as shown in the figure.

x0 = ?  m  
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 12.0 m/s. The cliff is h = 29.0 m above a flat, horizontal beach as shown in the figure. What are the coordinates of the initial position of the stone? What are the components of the initial velocity? Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable t be measured in seconds. Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. How long after being released does the stone strike the beach below the cliff? With what speed and angle of impact does the stone land? A place-kicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 21.6 m/s at an angle of 48.0 degree to the horizontal. By how much does the ball clear or fall short (vertically) of clearing the crossbar? (Enter a negative answer if it falls short.) Does the ball approach the crossbar (and cross above or beneath it) while still rising or while falling?

Explanation / Answer

a) x0 = 0

y0 = 29

b) v0x = 12
v0y = 0

c) vx = 12

vy = -9.81*t

d)
x = 12 t

y = 29 - 4.9 t^2

e)

0 = 29 - 4.9*t^2
t=2.43 s

f) vx = 12

vy = -9.81*2.43
vf = sqrt(12^2 + (9.81*2.43)^2)=26.7 m/s

angle = arctan(9.81*2.43/12)= 63.3 degrees

2) a) first x direction
36 = 21.6*cos(48 degrees)*t
t=2.49 s

now y direciton
y = 0 + 21.6*sin(48)*2.49 - 0.5*9.81*2.49^2= 9.55 m

so clears it by 9.55 = 3.05 = 6.5 m

b) vy = 21.6*sin(48) - 9.81*2.49=-8.37 m/s
so falling

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