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MArishka [77]
3 years ago
7

If you stand at the edge of a cliff that is 75 m high and throw a rock directly up into the air with a velocity of 20 m/s, at wh

at time will the rock hit the ground? (note: the quadratic formula will give two answers, but only one of them is reasonable.)
Physics
2 answers:
lesya [120]3 years ago
5 0

Answer:

  At time 6.45 seconds rock will hit ground.  

Explanation:

We have equation of motion , s= ut+\frac{1}{2} at^2, s is the displacement, u is the initial velocity, a is the acceleration and t is the time.

 Let us take up direction as positive, so displacement = -75 m, initial velocity = 20 m/s, acceleration = acceleration due to gravity = -9.8m/s^2

 Substituting

    -75= 20*t-\frac{1}{2} *9.8*t^2\\ \\ 4.9t^2-20t-75=0

    t = 6.45 seconds or t =-2.37 seconds

    Since negative time is not possible, t = 6.45 seconds.

    So at time 6.45 seconds rock will hit ground.

My name is Ann [436]3 years ago
4 0

The vertical position of the rock is given by:

y(t)=h+v_0 t -\frac{1}{2} gt^2

where

h=75 m is the initial height

v0=20 m/s is the initial vertical velocity

g=9.81 m/s^2 is the acceleration due to gravity

The problem asks to find the time t at which the rock hits the ground, so the time t at which y(t)=0, so the equation above becomes:

75 + 20 t - 4.9t^2 =0

Which has two solutions:

t=-2.37 s

t=6.45 s

The first solution is a negative time so it has no physical meaning, therefore the correct answer is t=6.45 s.


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