Answer
The astronaut's initial speed should be 4.8 m/s
Work Step by Step
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.
