Question

3. A rubber chicken is launched straight up at speed v from ground level. Find each of the following if the launch speed is tripled (in terms of any constants and v).
a. max height
b. hang time
c. impact speed

Answer 1

Given,

Initial launcher speed = v

If initial launcher speed =3v

a) Let, initially the maximum height was h, and finally it was H

Applying newton's law of motion,

$v^2= u^2-2gh$

Now, at the maximum height v=0

$\Rightarrow 0=v^2-2gh$

$h=\frac{v^2}{2gh}$

and finally $H=\frac{9v^2}{2g}$

b)

Let the time of hang is T, and time taken to reach at maximum height = t

Now, $v=u-gt$

at the top most point, final velocity of the object = 0

$\Rightarrow 0=v-gt$

$\Rightarrow t= \frac{v}{g}$

Hence, initially the time of flight of the projectile $(T)=2t = \frac{2v}{g}$

and for the final condition,

$T' = \frac{6v}{g}$

c)

The impact speed will be v if it was projected with v and it will be 3v, if it is projected with 3v.

but if $3v\ge V_{esc}$ ,

then it will not come back in the gravitational field.