SOLUTION: A body is projected downward at an angle of 30 tp the horizontal with a velocity of 9.8m/s ftom the top of the tower of 29.4m high .how long will it take before striking the ground

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Question 1040257: A body is projected downward at an angle of 30 tp the horizontal with a velocity of 9.8m/s ftom the top of the tower of 29.4m high .how long will it take before striking the ground?

Answer by ikleyn(52855)   (Show Source): You can put this solution on YOUR website!
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A body is projected downward at an angle of 30 to the horizontal with a velocity of 9.8 m/s from the top
of the tower of 29.4 m high. How long will it take before striking the ground?
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The body moves uniformly at the constant speed in horizontal direction and at the constant acceleration 
g =   downward in vertical direction.
     (! Do not miss the initial velocity 9.8  with the gravity acceleration g =   !)

To answer the question, it is enough to consider vertical movement of the body.

Its initial vertical velocity is  v =  =  =   directed downward.

Then an equation for the vertical coordinate of the body h(t) is

h(t) = ,

where g =    and  v =  ,  or

h(t) = .

Here h(t) is the vertical distance from the body to the ground level in meters, t is time in seconds.

To find the time moment when the body strikes the ground, you need to solve a quadratic equation 

h(t) = 0,  or   = .

It is the same as 

 = . 

The last equation is equivalent to 

 = .

Factor it. It is equivalent to

(t-3)*(t+2) = 0

and has the roots t = 3 and t = -2.

Only positive root is acceptable.

So, the answer is: t = 3.  The body hits the ground in 3 seconds.


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