Question

a body starts climbing up an inclined plane having inclination 30° and stops at a distance of 17.3 m. if the angle of inclination be 60° how long will it be able to climb up starting with the same speed :- (1) 8.6 m (2) 10.0 m (3) 12.9 m (4) 17.3 m

Answer 1

acceleration due to gravity along the inclined plane is given by

$a = -gsin\theta$

$a = -9.8*sin30 = -4.9 m/s^2$

now the stopping distance along the inclined plane is given by

d = 17.3 m

now using kinematics

$v_f^2 - v_i^2 = 2 a d$

$0^2 - v_i^2 = 2*(-4.9)*17.3$

$v_i = 13.02 m/s$

now if the angle of inclination is 60 degree

$a = - gsin60 = -8.49 m/s^2$

again by same kinematics equation

$v_f^2 - v_i^2 = 2 a d$

$0^2 - 13.02^2 = 2*(-8.49)*d$

$d = 10 m$

so it will stop after climbing up by 10m.