# A girl stands on top of the Golden Gate Bridge and throws a penny at a speed of 94.32km/hr at an angle of -68.8°. How long does it take the penny to fall the 224m to the San Francisco Bay?

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How far from the base of the bridge does it land?

What is the penny's velocity when it enters the water and at what angle?

How far from the base of the bridge does it land?

What is the penny's velocity when it enters the water and at what angle?

##### 1 Answer

Now initial velocity of projection

To calculate the time taken by the penny to fall to the bay we need to know its vertical velocity.

Which is

Applicable kinetic expression in the vertical direction is

# h = ut + 1/2 g t^2#

Taking origin at the location of girl and inserting given values and remembering that acceleration due to gravity

#-224 = -26.2 sin (68.8^@)t + 1/2 (-9.81) t^2#

# => t^2+4.98t -45.67=0#

Solving above quadratic using builtin graphics utility and ignoring the

#t=4.7\ s# , rounded to one decimal place.

The distance from the base of the bridge does it lands is given by the equation

#R="Horizontal Velocity"xx"time taken"#

#R=(26.2cos(-68.8^@))xx4.712=44.64\ m#

There is no change in the horizontal component of penny's velocity when it enters the water. Vertical component is found using the following kinematic expression.

#v=u+g t #

We get

#v_v=-26.2 sin (68.8)+-(9.81) xx4.712 #

#=>v_v=-24.427-43.282 #

#=>v_v=-67.709\ ms^-1#

Penny's velocity when it enters water

Magnitude of the final velocity

Angle of this velocity can be calculated with the help of