Q2. A 67 kg astronaut wants to jump over an 8.2 m-wide chasm on a distant planet without falling in. The acceleration due to gravity on this planet is g = 3.3 m/s2. a) If she leaps at a 20 angle, what initial speed does she need to clear the chasm? (Draw a sketch representing the problem using appropriate labels and coordinate system, and answer to three significant figures with the units). b) If she accidentally trips and falls straight down into the chasm with negligible air resistance, use Newton's laws to show that her free fall acceleration will be independent of her mass, and only depend on the planet's mass and radius (show the equations used and their names). c) If the mass of the planet is 7 x 1023 kg, what is its radius in meters? (Show the equations used and the algebra steps, and answer to 3 significant figures in scientific notation with the units). G = 6.67 x 10-11 Nm2/kg2