One of the primary goals of the Kepler space telescope is to search for Earth-like planets. Data gathered by the telescope indicates the existence of one such planet named Boralis orbiting a star 135 ly from our solar system. Consider an interstellar spaceship leaving Earth to travel to Boralis. The ship can reach 0.80c almost instantly and can also decelerate almost instantly. The ship is 143 m long in its reference frame.

1. What is the length of the moving ship (in m) as measured by observers on Earth?

2. How much time (in years) will it take for the spaceship to travel from Earth to Boralis, as measured by an observer on Earth?

3. How much time (in years) will it take for the spaceship to travel from Earth to Boralis, as measured by astronauts in the spaceship?

Which describes an image that can be produced by a concave lens? the image is real and smaller than the object. the image is virtual and larger than the object. the image is virtual and smaller than the object. the image is real and larger than the object.

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

70 give a real life example showing how sensory neurons work with the motor neurons