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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.