A free-body diagram of the block on the frictional part of the surface would show the force of friction acting in the opposite direction to the velocity of the block, and the force of gravity acting downward.
Using conservation of energy, the speed of the block at the base of the ramp can be found by setting the initial kinetic energy of the block (1/245^2) equal to the final kinetic energy of the block (1/2mv^2) and solving for v. v = sqrt((1/245^2)/(1/2*m)) where m is the mass of the block.
Using conservation of energy, the maximum vertical height H of the block on the ramp can be found by setting the initial potential energy of the block (mgH) equal to the final kinetic energy of the block (1/2mv^2) and solving for H. H = (1/2mv^2)/(m*g)
a) The total impulse given to the mass on the spring (mass A) during the brief collision is the product of the force exerted on the mass by the block and the time duration of the collision.
b) The speed of the mass on the spring (mass A) immediately after the collision can be determined using the conservation of momentum.
c) The velocity of the block immediately after the collision can also be determined using the conservation of momentum.
d) The spring constant can be determined by using the equation k = (2*F)/x, where F is the force exerted on the spring and x is the compression of the spring.
To find the horizontal range of the block from the end of the ramp, we can use the equations for horizontal and vertical motion of a projectile, with the angle of launch being 30 degrees, the initial speed being 6 m/s, and the final vertical position being 1m above the end of the ramp.