Assume that a vaulter is able to carry a vaulting pole while running as fast as Carl Lewis in his world record 100-m dash (around 12 m/s). Also assume
that all of the vaulter's kinetic energy is transformed into gravitational
potential energy. What vaulting height could that person attain?
(Hint: Use the equation 1/2 mv^2? = mgh.)

Two loudspeakers, 5.5 m apart and facing each other, play identical sounds of the same frequency. you stand halfway between them, where there is a maximum of sound intensity. moving from this point toward one of the speakers, you encounter a minimum of sound intensity when you have moved 0.33 m . assume the speed of sound is 340 m/s.part a) what is the frequency of the sound? part b) if the frequency is then increased while you remain 0.21 m from the center, what is the first frequency for which that location will be a maximum of sound intensity? express your answer to two significant figures and include the appropriate units.

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.

Avector a⃗ has a length of 8.6 m and points in the negative x direction. find the x component of the vector −3.7a⃗ .