Question* An a-particle moving at a speed of $1.0 \times 10^{6} \mathrm{~ms}^{-1}$ collides with a stationary proton. After willitin The proton travels with a speed of $1.88 \times 10^{6} \mathrm{ir}$ in the divectuon in which the $G$-particle. war travelling. Calculate the boed of the $x$-partels offer collim. [Marie of $\alpha$-partido $=6.64 \times 10^{-23} 9$ Nas of prite $=166 \times 10^{-64} \mathrm{~kg}$

Studdy Solution
Solve for the speed of the alpha particle after the collision ($v_{1f}$):
First, simplify the equation:
$$6.64 \times 10^{-21} = 6.64 \times 10^{-27} \times v_{1f} + 3.1208 \times 10^{-21}$$
Rearrange to solve for $v_{1f}$:
$$6.64 \times 10^{-21} - 3.1208 \times 10^{-21} = 6.64 \times 10^{-27} \times v_{1f}$$
$$3.5192 \times 10^{-21} = 6.64 \times 10^{-27} \times v_{1f}$$
$$v_{1f} = \frac{3.5192 \times 10^{-21}}{6.64 \times 10^{-27}}$$
$$v_{1f} \approx 5.30 \times 10^{5} \, \text{m/s}$$
The speed of the alpha particle after the collision is approximately:
$$\boxed{5.30 \times 10^{5} \, \text{m/s}}$$