| 1) Use the following two kinematics equations to show that the above projectile follows a parabolic path. |
Δy = vi Δt + 1/2gΔt2 |
| Δx = vaveΔt |
| vH = Δx/Δt = vRcosθ |
| Δt = Δx/(vRcosθ) |
Δy = viΔt + 1/2gΔt2 = vRsinθΔt - 1/2gΔt2 |
| Substituting Δt = Δx/(vRcosθ) yields: |
| Δy = vRsinθ•Δx/(vRcosθ) - 1/2g•Δx2/(vR2cos2θ) |
| Δy
= |
| Δy = tanθ•Δx - g•Δx2/(2vR2cos2θ) |
| Δy = ax - bx2 |
| where a = tanθ and b = -g/(2vR2cos2θ) are constants in the absence of air resistance. |
| 2) A space-flight projectile is launched in a parabolic trajectory. An astronaut in this practice capsule feels |
| weightless. |
| (a) Why? |
| In the absence of air resistance, a projectile is in free fall because the only force acting on it is its |
| weight, Fw. |
| (b) In what sense is he weightless? |
| He is weightless in the sense that he could not exert a force on a scale because both he and the scale |
| are accelerating at the same rate, -g. Although his apparent weight is zero due to his vertical |
| acceleration he is not truly weightless. If he was truly weightless, then as a result of his launch, he |
| would continue to move in a straight line at constant speed indefinitely in the absence of air resistance |
| or any external force. |