A diver is standing at the edge of a diving board that is 15 m above the surface

Question

A diver is standing at the edge of a diving board that is 15 m above the surface of the pool. She launches herself upwards with an initial speed of 5 m/s.

a. What is her velocity at maximum height?

b. When will she reach maximum height?

c. What is her acceleration at maximum height?

d. How high above the diving board will she be at maximum height?

e. When will she hit the water?

f. How fast will she be moving just before she enters the water?

g. What is her acceleration just before hitting the water?

h. What is her acceleration after entering the water if she travels 5 m down into the pool before stopping?

Explanation / Answer

a) What is her velocity at maximum height?
sol. at maximum height velocity will become zero
b. When will she reach maximum height?
sol. intial velocity u = 5 m/s acceleration is only due to gravity which is down ward so a = -g = -9.8 m/s2

t = u/g = 5/9.8 = 0.51 s
c. What is her acceleration at maximum height?
sol. her accelaration remains same at every point in her flight as there are no external forces so acceleration is -g that is g downwards
d. How high above the diving board will she be at maximum height?
sol. vertical distance travelled during the time is h = ut - 1/2 g t2

h=5*0.51 - 1/2 * 9.8 (0.51)2 = 1.325 m
e. When will she hit the water?
sol. now she is at height of 15m+1.325m = 16.325 m and only thing she has is acceleration due to gravity g

so 1/2 *g*t2= 16.325m => t = (2*16.325/9.8) = 1.825 s
f. How fast will she be moving just before she enters the water?
sol. as we know v = u+at => u=0 and a = -g so V= -9.8 * 1.825 = 17.88 m/s downward velocity
g. What is her acceleration just before hitting the water?
sol. acceleration does not change as there are no force so still same g downwards
h. What is her acceleration after entering the water if she travels 5 m down into the pool before stopping?

sol. supposing there is no buyont force from water so no external foreces even at depth of 5m so still same

but in practical there will be water friction and buyont force so acceleration will no longer remains g

please try to keep the questions in parts

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