A radar tracks the flight of a projectile (see Figure P3.6). At time t, the radar measures the horizontal component vx(t) and the vertical component vy(t) of the projectile's velocity and its range R(t) and elevation ϕ(t). Are these measurements sufficient to compute the horizontal distance D from the radar to the launch point of the projectile? If so, derive the expression for D as a function of g and the measured values vx(t), vy(t), R(t), and ϕ(t).
![A penguin of 7 kg stands at the edge of an ice cliff and dives into the ocean below. The penguin has an initial velocity of 5 ms−1 and at an angle of 60∘ with respect to the horizontal. The cliff is 15 m above the water level. Assume air resistance is negligible and take the value of the acceleration due to gravity as 9.81 ms−1. Calculate: a) The time it takes for the penguin to hit the water. [3 marks] b) The horizontal distance travelled by the penguin before hitting the water. [2 marks] c) The velocity of the penguin just before hitting the water. [3 marks] d) The momentum of the penguin in unit vector notation at the highest point (with respect to the water level) of its projectile. [2 marks] e) Supposed that upon splashing on the water, the magnitude of the vertical component of the velocity found in part (c) above is being reduced by half in 0.2 seconds while the horizontal component remained the same, determine the impulsive force experience by the penguin. [2 marks].](https://www.doubtrix.com/uploads/editor/7669666301lraWjZPvzV.jpg)
