1. A futuristic spaceship flies past Pluto with a speed of 0.964c relative to the surface of the planet. When the spaceship is directly overhead at an altitude of 1500km, a very bright signal light on the surface of Pluto blinks on and then off. An observer on Pluto measures the signal light to be on for 80 us. What is the duration of the light pulse as measured by the pilot of the spaceship? 2. Inside a spaceship flying past the earth at three-fourths the speed of light, a pendulum is swinging. (a) if each swing takes 1.5 s as measured by an astronaut performing an experiment inside the spaceship, how ling will the swing take as measure by a person at mission control who is watching the experiment? (b) If each swing takes 1.5 s as measured by a person at mission control on earth, how ling will it take as measured by the astronaut in the spaceship? 3. An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.19 s. The first officer on the craft measures the searchlight to be on for 12 ms. (a) Which of these two measure times is the proper time? (b) what is the speed of the spacecraft relative to the earth, expressed as a fraction of the speed of light, c? 4. You measure the length of a futuristic car to be 3.6 m when the car is at rest relative to you. If you measure the length of the car as it zooms past you at a speed of 0.9c, what result do you get? 5. A meterstick moves past you at great speed. If you measure the length of the moving meterstick to be 1 ft, at what speed is the meterstick mobbing relative to you? 6. A rocket ship flies past the earth with a velocity of .85c. Inside, an astronaut who is undergoing a physical examination is having his height measured while he is lying down parallel to the direction the rocket ship is moving. (a) If his height is measured to be 2 m by his doctor inside the ship, what would a person watching this from earth measure for his height? (b) if the earth- based person had measured 2 m, what would the doctor in the spaceship have measured for the astronaut's height