Question

MIT’s robot cheetah can jump over obstacles 46 cm high and has speed of 12.0 km/h. (a) If the robot launches itself at an angle of 60° at this speed, what is its maximum height? (b) What would the launch angle have to be to reach a height of 46 cm?

a) 0.889 m, 45°
b) 1.032 m, 55°
c) 1.172 m, 65°
d) 1.315 m, 75°

Answer 1

The maximum height of the robot cheetah launched at an angle of 60° is approximately 0.889 m. The launch angle required to reach a height of 46 cm is approximately 45°.

Step-by-step explanation:

To calculate the maximum height of the robot cheetah when launched at an angle of 60°, we need to use the equation for maximum height: H = (v2sin2(θ))/(2g), where H is the maximum height, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. The initial velocity can be calculated using the given speed of 12.0 km/h and the launch angle. The acceleration due to gravity is approximately 9.8 m/s2. Plugging in the values, the maximum height is approximately 0.889 m.

To find the launch angle required to reach a height of 46 cm, we can rearrange the equation for maximum height to solve for the launch angle: θ = arcsin(sqrt((2HG)/(v2))), where H is the desired height and G is the acceleration due to gravity. Plugging in the values, the launch angle is approximately 45°.