Question

Three balls are thrown off a tall building with the same speed but in different directions. Ball A is thrown in the horizontal direction; ball B starts out at 45° above the horizontal; ball C begins its flight at 45° below the horizontal. Which ball has the greatest speed just before it hits the ground? Assume that the ground near the building is level, and ignore any effects due to air resistance.1. Ball A2. Ball B3. Ball C4. Balls B and C have the same speed, which is greater than Ball A5. All balls have the same speed

Answer 1

Answer:All balls have same velocity

Explanation:

Ball A

horizontal velocity$\left ( u_x\right )=u$

vertical velocity$\left ( u_y\right )=0$

let h be the height of building

Vertical velocity acquired by Ball A

$u_y=\sqrt{2gh}$

Velocity just before hitting ground=$\sqrt{u^2+2gh}$

Ball B

launched with velocity u at angle of 45 above horizontal

$u_x=ucos45$

$u_y=usin45$

horizontal velocity will remain same as there is no acceleration in that direction

vertical velocity just before hitting the floor

$u_{yf}^2=\left ( usin45\right )^2+2gh$

$u_{yf}=\sqrt{\frac{u^2}{2}+2gh}$

Final velocity before hitting ground $v=\sqrt{u^2+2gh}$

Ball C

$u_x=ucos45$

$u_y=-usin45$

horizontal velocity will remain same as there is no acceleration in that direction

vertical velocity just before hitting the floor

$u_{yf}^2=\left ( -usin45\right )^2+2gh$

$u_{yf}=\sqrt{\frac{u^2}{2}+2gh}$

Final velocity before hitting ground $v=\sqrt{u^2+2gh}$

Thus all three balls will have same final velocity.