A ball is projected horizontally from an incline so as to strike a cart slinding frictionlessiy in the incline \( 6 m \) away (as shown). At the instance the ball is thrown, the speed of cart is ' \( u \) ' (in \( m / s \) ). T value of ' \( u \) ' so that the ball strikes the cart.(neglect height of cart and point of projection'of ball above the incline)

Question

A ball is projected horizontally from an incline so as to strike a cart slinding frictionlessiy in the incline \( 6 m \) away (as shown). At the instance the ball is thrown, the speed of cart is ' \( u \) ' (in \( m / s \) ). T value of ' \( u \) ' so that the ball strikes the cart.(neglect height of cart and point of projection'of ball above the incline)

Answer 1

resolve all movement perpendicular and along the incline 

therefore along the incline: 

=> a = gsin37°, initial velocity u = 10cos37° 

| to the incline: 

=> a = gcos37°, initial velocity u'' = 10sin37° 

time taken to return to incline = t = 2u''/(gcos37°) = 20tan37°/g ~= 1.54 s 

in this time the cart travels to a distance = 6 + v[1.54] from the projection point. 

to reach the cart therefore => 

6 + 1.54v = 10cos37°(1.54) + ½9.81sin37°(1.54)² 

=> 6.97 + 12.27 - 6 = 1.54v 

=> v ~= 9 m/s