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Chapter 3: Problem 10
You're in a bus moving with constant velocity on a level road when you throw a ball straight up. When the ball returns, does it land ahead of you, behind you, or back at your hand? Explain.
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Estimate the acceleration of the Moon, which completes a nearly circular orbit of 384.4 Mm radius in 27 days.
The portion of a projectile's parabolic trajectory in the vicinity of the peak can be approximated as a circle. If the projectile's speed at the peak of the trajectory is \(v\), formulate an argument to show that the curvature radius of the circle that approximates the parabola is \(r=v^{2} / g\)
A particle's position is \(\vec{r}=\left(c t^{2}-2 d t^{3}\right) \hat{\imath}+\left(2 c t^{2}-d t^{3}\right) \hat{\jmath}\) where \(c\) and \(d\) are positive constants. Find expressions for times \(t>0\) when the particle is moving in (a) the \(x\) -direction and (b) the \(y\) -direction.
Derive a general formula for the horizontal distance covered by a projectile launched horizontally at speed \(v_{0}\) from height \(h\)
Which of the following are legitimate mathematical equations? Explain. (a) \(v=5 \hat{i} \mathrm{m} / \mathrm{s} ;\) (b) \(\vec{v}=5 \mathrm{m} / \mathrm{s} ;\) (c) \(\vec{a}=d v / d t\) (d) \(\vec{a}=d \vec{v} / d t ;\) (e) \(\vec{v}=5 \hat{i} \mathrm{m} / \mathrm{s}\)
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