Question

1. A single force F(x) = −8.0x (in newtons) acts on a 3.0-kg body. When x = 6.75 m, the speed of the body is 4.0 m/s. What is its speed at x = 2.5 m?
2. A T-shirt cannon launches a shirt at 8.00 m/s from a platform height of 5.00 m from ground level. How fast will the shirt be traveling if it is caught by someone whose hands are (a) 2.00 m from ground level? (b) 4.00 m from ground level? Neglect air drag.

Answer 1

1)

$$0.5mv^2+0.5kx^2=0.5mv'^2+0.5kx'^2\\ (8)(4)^2+(3)(6.75)^2=(8)v'^2+(3)(2.5)^2\\v'=5.5\frac{m}{s}$$

2) a)

$$v^2-8^2=2(9.8)(5-2)\\v=11.1\frac{m}{s}$$

b)

$$v^2-8^2=2(9.8)(5-4)\\v=9.14\frac{m}{s}$$