A sled with rider having a combined mass of 120 kg travels over the perfectly smooth icy hill shown in the accompanying figure. How far does the sled land from the foot of the cliff (in m)?

sjeikdom0
2021-01-24
Answered

You can still ask an expert for help

au4gsf

Answered 2021-01-25
Author has **95** answers

The rider begins with

$KE=\frac{1}{2}m{v}^{2}=0.5\left(120kg\right){\left(22.5\frac{m}{s}\right)}^{2}=30375\text{}J$

and

$PE=mgh=120\cdot 9.8\cdot 0=0$

so,

${E}_{t}=KE=30375\text{}J$

where

KE=kinetic energy

PE=potential energy

E=total energy=KE+PE

At the top of the hill some of the KE is turned into PE=mgh

PE becomes

$PE=120kg\cdot 9.8\frac{m}{{s}^{2}}\cdot 11.0m=12936\text{}J$

and since total energy is conserved KE becomes

$KE={E}_{t}-PE=30375\text{}J-12936\text{}J=17439\text{}J$

$KE=\frac{1}{2}m{v}^{2}\Rightarrow v=\sqrt{\frac{2\cdot KE}{m}}=\sqrt{\frac{2\cdot 17439}{120}}=17.05\text{}\frac{m}{s}$

Now since the hill is 11.0 m high the period of time of thevertical fall is given by

$h={v}_{0}t+\frac{1}{2}a{t}^{2}$

h=11.0m

${v}_{0}=0$ (this is the initial vertical velocity)

a=9.8m/s

solve for t using the quadratic formula

$t=\frac{-{v}_{a}\pm \sqrt{{v}_{0}^{2}-4\left(\frac{1}{2}a\right)(-h)}}{2\left(\frac{1}{2}a\right)}$

$t=\pm \frac{\sqrt{2ah}}{a}$

choose the positive answer, as the negative answer for time is meaningless

$t=\frac{\sqrt{2\left(9.8\right)\left(11\right)}}{9.8}=1.498s\approx 1.5\text{}\mathrm{sec}$

so we know it takes 1.5 sec to hit the ground and we know the horizontal velocity is v=17.05m/s, distance travelled before impact:

$d=vt=17.05\frac{m}{s}\text{}\cdot 1.5s=25.5m$

and

so,

where

KE=kinetic energy

PE=potential energy

E=total energy=KE+PE

At the top of the hill some of the KE is turned into PE=mgh

PE becomes

and since total energy is conserved KE becomes

Now since the hill is 11.0 m high the period of time of thevertical fall is given by

h=11.0m

a=9.8m/s

solve for t using the quadratic formula

choose the positive answer, as the negative answer for time is meaningless

so we know it takes 1.5 sec to hit the ground and we know the horizontal velocity is v=17.05m/s, distance travelled before impact:

asked 2021-02-22

The spring of a spring gun has force constant k =400 N/m and negligible mass. The spring is compressed 6.00 cm and a ball with mass 0.0300 kg is placed in the horizontal barrel against the compressed spring.The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 6.00 cm long, so the ball leaves the barrel at the same point that it loses contact with the spring. The gun is held so the barrel is horizontal. Calculate the speed with which the ballleaves the barrel if you can ignore friction. Calculate the speed of the ball as it leavesthe barrel if a constant resisting force of 6.00 Nacts on the ball as it moves along the barrel. For the situation in part (b), at what position along the barrel does the ball have the greatest speed?

asked 2021-02-13

A rocket is launched at an angle of 53 degrees above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s a long its initial line of motion with an acceleration of 30.0 m/s/s. At this time, its engines fail and the rocket proceeds to move as a projectile. Find:

a) the maximum altitude reached by the rocket

b) its total time of flight

c) its horizontal range.

asked 2021-02-25

A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?

asked 2020-10-21

An 80.0-kg skydiver jumps out of a balloon at an altitude of1000 m and opens the parachute at an altitude of 200 m. (a) Assuming that the total retarding force on the diver is constant at 50.0 N with the parachute closed and constant at 3600 N with the parachute open, what is the speed of the diver whenhe lands on the ground? (b) Do you think the skydiver will be injured? Explain. (c) At what height should the parachute be opened so that the final speed of the skydiver when he hits the ground is 5.00m/s? (d) How realistic is the assumption that the total retarding force is constant? Explain.

asked 2021-01-22

Tell whether the function represents exponential growth or exponential decay.

asked 2022-04-25

which statement about ⅔ is true

asked 2022-01-29

How do you write $y+\frac{1}{3}=\frac{1}{4}(x-3)$ in standard form?