When traveling through mountains, most highways periodically have emergency escape ramps to allow large, heavy vehicles to stop safely, even when their brakes are not working properly. One such escape ramp is angled 13 ∘ above the horizontal. The brakes on one large truck (mass 1.4×104 kg ) fail when driving at a speed of 80 miles per hour (35.75 m/s), and the driver makes use of the escape ramp.

Part A: What is the minimum length of ramp necessary for this truck to come to a stop? Assume negligible friction and air resistance forces.

Part B: If instead dissipative forces (friction and air resistance) provide a constant force of 60,000N parallel to the ramp, what is the minimum length of ramp necessary for this truck to come to a stop?

my answer for part A is 290 m, but I am unsure how to get the answer for part B. please help

Bag of bolts weight 29.4n

Hypothesis. why don’t you know this? i learned this stuff in like 5th grade

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s