Throwing rocks

Classical Mechanics Level 2

First, I threw a rock towards north with speed $50 \text{ m/s}$ , initially making an angle of $40^\circ$ with the vertical. Two seconds later, I threw another rock towards east with speed $100 \text{ m/s}$ , making an initial angle of $70^\circ$ with the vertical.

What path would the first rock appear to move in, if we looked at it in the reference frame of the second rock?

Straight line The rock would appear to be stationary Parabola Circle

1 solution

Pranshu Gaba
Apr 20, 2016

Let $\hat{i}$ , $\hat{j}$ , and $\hat{k}$ be unit vectors in the east, north and up direction respectively. We will now write the positions of both rocks as a function of time.

Rock 1: $\vec{v_1} (t)= 50 \sin(40^\circ) \ \hat{j} + (50 \cos(40^\circ) - gt)\ \hat{k}$
Rock 2: $\vec{v_2} (t) = 100 \sin(70^\circ) \ \hat{i} + (100 \cos(70^\circ) - g(t-2))\ \hat{k}$

The velocity of rock 1 in the reference frame of rock 2 is given by $\vec{v_1} - \vec{v_2}$ .

$\vec{v_1} - \vec{v_2} = 50 \sin(40^\circ) \ \hat{j} - 100 \sin(70^\circ) \ \hat{i} + (50 \cos(40^\circ) - 100 \cos(70^\circ) + 2g) \hat{k}$

Note that $\vec{v_1} - \vec{v_2}$ is non-zero, and does not change with time. This means that in the reference frame of the second rock, the first rock will appear to move in a straight line . $_\square$

Throwing rocks

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