Question

need help ASAP

3 2. A block of mass m = 2.00 kg is released from rest at h = 0.500 m above the surface of a table, at the top of a = 30.0 incline. The frictionless incline is fixed on a table of height H = 2.00 m. Show your work and use significant figures in your final answer. a. What is the velocity of the block as it leaves the incline? (6 Points) b. How far from the table will the block hit the floor? (6 Points)

Answer 1

Q.2A) Using conservation of energy

$\frac{1}{2}mv^2 = mgh$

$v= \sqrt{2gh} \\ v = \sqrt{2 \times 9.8 \ \rm m/s^2 \times 0.500 \ \rm m} \\ v = 3.13 \ \rm m/s$30⁰ below the horizontal.

Q2B) Let us first calculate the time taken by the block to reach the ground

$\\ H = v\sin \theta t + \frac{1}{2}gt^2 \\ 2.0 \ \rm m = 3.13 \ \rm m/s \sin 30^{\circ} \times t+ \frac{1}{2} \times 9.8 \ \rm m/s^2 \times t^2 \\ 4.9t^2 + 1.565 t -2 = 0 \\$

Solving this equation

$t = 0.50 \ \rm s, -0.82 \ \rm s$

Taking the positive value of time only

$\\ R = v\cos \theta .t \\ R = 3.13 \ \rm m/s \times \cos30^{\circ} \times 0.50 \ \rm s \\ R = 1.36 \ \rm m$