Question

water balloons are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed when it hits the ground? Ignore air resistance.

Answer 1

Answer:

90°/-90°

Explanation:

assume we are measuring launch angles with respect to horizontal surface

assume +y direction to be positive

when object is launched with launch angle <90° but >0°

it has 2 components for velocity v

$v_{x}$ in horizontal direction

$v_{y}$ in vertical direction

the $v_{x}$  component remains unchanged throughout the travel as there is no force acting on it to change it (air resistance is ignored)

$v_{y}$ this component is decreased till 0, as acceleration due to gravity is acting on it and starts to increase in downward direction.

when ball reaches the same height of the building while going down, this vertical component of ball is equal same as $v_{y}$ but in opposite direction

so now vertical velocity = -$v_{y}$

this component keeps on increasing until it hits the ground as the gravity accelerates it to the ground

the horizontal component is unchanged throughout

So to have maximum speed when the ball reaches the ground,the vertical velocity component must be maximum at launch,so it will just be accelerated until it hits the ground.

⇒ In this case,the maximum vertical component can be v or -v

⇒$v_{y}$=v or $v_{y}$= -v

⇒ horizontal component is 0

this means  that ball is thrown directly up at 90° or directly down at 90° with respect to horizontal.