In a grocery store you push a 12.5 kg shopping cart

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

The astronauts on the space shuttle flights experienced an acceleration of 29 m/s2 (about 3 "g's") during lift-off. what upward force must the astronaut's seat apply to the astronaut in order to cause this acceleration? assume the astronaut's mass is 70 kg, and compute this force when the acceleration is near the earth's surface so their weight equals latex: mg m g .

The particle p starts from rest at point a at time t = 0 and changes its speed thereafter at a constant rate of 2.8g as it follows the horizontal path shown. determine the magnitude and direction of its total acceleration (a) just before point b, (b) just after point b, and (c) as it passes point c. state your directions relative to the x-axis shown (ccw positive) and choose the angle with the smallest magnitude.