(a) Is mechanical energy conserved? YesNo (b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (Use the following as necessary: height h, mass m, and gravitational acceleration g.) potential energy kinetic energy top of the waterslide launching point in the pool (c) Determine her initial speed v0 at the launch point in terms of g and h. v0 =
(a) Is mechanical energy conserved? YesNo (b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (Use the following as necessary: height h, mass m, and gravitational acceleration g.) potential energy kinetic energy top of the waterslide launching point in the pool (c) Determine her initial speed v0 at the launch point in terms of g and h. v0 =
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A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (see figure). She is launched from a height h/5 into the pool.
An illustration shows a child sliding down a curved slide next to a swimming pool. The slide has a horizontal rest at the top, at the height of h from the ground. The slide then has a steep dip down to the ground, where it curves again and goes upward to a height h/5 and ends there. The child is shown as being launched from this height into the air over the pool. The parabolic path the child takes through the air starts at an angle ? with the horizontal. The maximum height of this path above the water is labeled ymax.
(a) Is mechanical energy conserved?
(b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (Use the following as necessary: height h, mass m, and gravitational acceleration g.)
(c) Determine her initial speed v0 at the launch point in terms of g and h.
(d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, v0x.
(e) Use the x-component of the answer to part (c) to eliminate v0 from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle ?.
YesNo
(b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (Use the following as necessary: height h, mass m, and gravitational acceleration g.)
| potential energy | kinetic energy | |
| top of the waterslide |
|
|
| launching point |
|
|
| in the pool |
|
|
(c) Determine her initial speed v0 at the launch point in terms of g and h.
v0 =
(d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, v0x.
ymax =
(e) Use the x-component of the answer to part (c) to eliminate v0 from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle ?.
ymax =
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