select the correct answer.\na ball is ejected to the right with an unknown horizontal velocity from the top…

select the correct answer.\na ball is ejected to the right with an unknown horizontal velocity from the top of a pillar that is 50 meters in height. at the exact instant, a carriage moving on rails is also released to the right from the bottom of the pillar. calculate the velocity with which the carriage should be released so that the ball falls in the carriage after the carriage has traveled a distance of 50 meters on the ground.\na. 12.20 meters/second\nb. 13.23 meters/second\nc. 14.30 meters/second\nd. 15.65 meters/second\ne. 16.00 meters/second

select the correct answer.\na ball is ejected to the right with an unknown horizontal velocity from the top of a pillar that is 50 meters in height. at the exact instant, a carriage moving on rails is also released to the right from the bottom of the pillar. calculate the velocity with which the carriage should be released so that the ball falls in the carriage after the carriage has traveled a distance of 50 meters on the ground.\na. 12.20 meters/second\nb. 13.23 meters/second\nc. 14.30 meters/second\nd. 15.65 meters/second\ne. 16.00 meters/second

Answer

Explanation:

Step1: Calculate time for ball to fall

The ball is in free - fall in the vertical direction. The height of the pillar $h = 50$ m. Using the equation $h=\frac{1}{2}gt^{2}$ (where $g = 9.8$ m/s²), we can solve for time $t$. Rearranging the formula gives $t=\sqrt{\frac{2h}{g}}$. $t=\sqrt{\frac{2\times50}{9.8}}\approx\sqrt{\frac{100}{9.8}}\approx 3.19$ s.

Step2: Calculate carriage velocity

The carriage travels a distance $d = 50$ m in time $t$. Using the formula $v=\frac{d}{t}$, substituting $d = 50$ m and $t\approx3.19$ s, we get $v=\frac{50}{3.19}\approx15.65$ m/s.

Answer:

D. 15.65 meters/second