I have a basic kinematics problem about a ball thrown upward.?

Question

A ball thrown upwards at a speed of 15m/s at the edge of a 100m high building. How long does it take to reach the ground if it just misses the edge of the building on the way down?

Answer 1

the basic kinematic equation is:

y=y0+v0*t-g/2*t^2

where y is distance from the point of release, y0 is the initial height, v0 is the initial velocity, g is the gravitational acceleration (9.8 m/s^2) and t is the time. We must choose an axis system. Since this is a 1D problem we can choose the direction up as positive and down as negative (this has already been put into the kinematic equation notice the minus sign before the constant g, indicating that the downward acceleration is in the negative direction. According to the problem at hand y0=100, v0=15 and g=10 m/s^2 (roughly). We want to know at what t, y=0? Put this into the equation and we have

0=100+15*t-5*t^2

t^2-3t-20=0

this is a quadratic equation with 2 solutions.

1) t<0, this is impossible because the ball could not have reached the bottom before it was thrown

2) t=6.2 seconds. This is the right answer

Answer 2

Th first equation to be used is

v = u + at

where

v is the final velocity

u is the initial velocity

a si the acceleration and

t is the time taken

In this case, since the ball is going up, it decelerates (opp of accelerates)

hence a is -ve.

Also, the value of a is the acceleration due to Earth's gravity, which is 9.81 m / sec^2

When the ball reaches the top, its velocity (final velocity v) is 0

substituting, we get

0 = 15 - 9.81 x t

or t = 15 / 9.81 = 1.53 seconds

Also, v^2 = u^2 - 2 x a x s

where s is the distance travelled.

For this case,

0^2 = 15^2 - 2 x 9.81 x s

or s = 15^2 /(2 x 9.81)

s = 11.47 m

Now the ball is at an elevation of 111.47 (100 m of building + 11.47 m travelled upwards).

When it starts falling down, its initial velocity is 0

Now s = ut + 1/2 x a x t^2

111.47 = 0 + 1/2 x 9.81 x t^2

or t = sqrt(111.47 x 2 / 9.81) = 4.767 seconds

So the total time taken = 1.53 + 4.767 = 6.297 seconds

Hope it is clear.