To win the game, a place kicker must kick a
football from a point 19 m (20.7784 yd) from
the goal, and the ball must clear the crossbar,
which is 3.05 m high. when kicked, the ball
leaves the ground with a speed of 15 m/s at
an angle of 51.7
◦
from the horizontal.
the acceleration of gravity is 9.8 m/s
2
.
by how much vertical distance does the ball
clear the crossbar?
answer in units of m.

An asteroid is discovered in a nearly circular orbit around the sun, with an orbital radius that is 2.47 times earth's. what is the asteroid's orbital period, its "year," in terms of earth years?

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Aprojectile is launched from ground level with an initial velocity of v 0 feet per second. neglecting air resistance, its height in feet t seconds after launch is given by s equals negative 16 t squared plus v 0 t. find the time(s) that the projectile will (a) reach a height of 192 ft and (b) return to the ground when v 0equals112 feet per second. (a) find the time(s) that the projectile will reach a height of 192 ft when v 0equals112 feet per second. select the correct choice below and, if necessary, fill in the answer box to complete your choice.