A child starts from rest and slides without friction from a height of h = 8.0 m

Question

A child starts from rest and slides without friction from a height of h = 8.0 m along a slide next to a pool (see figure). She is launched from a height of 1.6 m (ignore the h/5 in the figure) at an angle of 24° into the air over the pool.

What is her maximum height above the water after leaving the slide? Hint: it is possible to do this without doing projectile motion, even desirable as we are trying to learn conservation of energy; this problem does require you to use conservation of energy more than once.
???? m

Explanation / Answer

given,

height h=8m

angle theta=24 degrees

noe,

at top of the slide:

potential energy P.E=m*g*h

kinetic energy K.E=0

and Total enrgy T=m*g*h+0 =m*g*h

at launching point:

Total energy,T=m*g*h

P.E=m*g*h/5

K.E=T-P.E=m*g*h-(m*g*h/5)

K.E=(m*g*4h/5)

let, vo is speed at launching point

1/m*vo^2=(m*g*4h/5)

====>

vo=sqrt(8gh/5) -----------(1)

let,

vox is speed at maximum height of y_max

then, x-component of vo is ,

vox=vo*cos(theta)

vox=sqrt(8gh/5)*cos(theta) ------(2)

and

P.E+K.E=T

m*g*y_max+1/2*m*vox^2=m*g*h

=====>

y_max=h-[(1/2g)*vox^2] --------(3)

from equation no (2) and (3)

y_max = h-[(1/2g)*(8gh/5)*cos^2(theta)]

y_max = h-[(8h/10)*cos^2(theta)]

now,

y_max = 8-[(8*8/10)*cos^2(24)]

=2.66 m -----------------------------------is answer

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.