## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

We can use the astronaut's weight to find the acceleration due to gravity $g_p$ on this planet; $weight = m~g_p$ $g_p = \frac{weight}{m}$ $g_p = \frac{180~N}{55~kg}$ $g_p = 3.27~m/s^2$ We can use the equation for the horizontal range $x$ to find the required initial speed; $x = \frac{v_0^2~sin(2\theta)}{g_p}$ $v_0^2 = \frac{x~g_p}{sin(2\theta)}$ $v_0 = \sqrt{\frac{x~g_p}{sin(2\theta)}}$ $v_0 = \sqrt{\frac{(3.5~m)(3.27~m/s^2)}{sin[(2)(15^{\circ})]}}$ $v_0 = 4.8~m/s$ The astronaut's initial speed should be 4.8 m/s.