Ashell is fired from the ground with an initial speed of 1.60 × 103 m/s (approximately five times the speed of sound) at an initial angle of 51.0 ◦ to the horizontal. the acceleration of gravity is 9.81 m/s 2 . a) neglecting air resistance, find the shell’s horizontal range. answer in units of m.

Aplayground slide is 8.80 ft long and makes an angle of 25.0° with the horizontal. a 63.0-kg child, initially at the top, slides all the way down to the bottom of the slide. (a) choosing the bottom of the slide as the reference configuration, what is the system's potential energy when the child is at the top and at the bottom of the slide? what is the change in potential energy as the child slides from the top to the bottom of the slide? (include the sign of the value in your answer.)