1. An Astronaut standing on the moon's surface (no atmosphere) launches a small ball straight upwards with an initial velocity of +5.0 m/s. On the moon surface the acceleration due to gravity is g=1.62 m/s^2. A. Determine how high the ball travels and find numerically (3 sig. figs.) how high the ball goes. (show work as needed) (t= 6.016 sec)

B. If our astronaut doubled the speed of the upwards toss, by what factor would the high of the projectile increase? Variables can be helpful here if you know how to take ratios.

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 ⇒

An architect plans to use solar energy to heat the next house he designs. what principle of absorption and infrared energy can be applied to the design of the new house? how could she apply to those principals?

A10-kg piece of aluminum sits at the bottom of a lake, right next to a 10-kg piece of lead, which is much denser than aluminum. which one has the greater buoyant force on it? explain. b - the aluminum a) both have the same buoyant force. b) the aluminum c) the lead d) it cannot be determined without knowing their volumes.