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At what height would the gravitational potential energy have a value of 73.7 joules for a 15 kilogram object? Note that acceleration due to gravity is 9.8 meters/second2.. A. 0.5 meters. B. 1.2 meters. C. 2.0 meters. D. 3.1 meters. E. 3.4 meters

Verified Answer :

HomertheGenius

Acceleration due to gravity: g = 9.8 m/s²;
h - height;
m - mass, m = 15 kg;
E p - potential energy; E p = 73.7 J
E p = m · g · h
h = E p / (m · g)
h = 73.7 J / ( 15 kg· 9.8 m/s² ) = 73.7 / 147 = 0.5 m
Answer: A ) 0.5 meters

Answer:

Option A is correct

0.5 m

Step-by-step explanation:

Potential energy(P.E.) is given by:

\(P.E = mgh\)                ....[1]

where,

m is the mass

g is the acceleration due to gravity

h is the height.

As per the statement:

Potential energy have a value of 73.7 joules for a 15 kilogram object.

⇒\(P.E. = 73.7 J\) and m = 15 kg

Use: g = 9.8 m/s^2

Substitute these in [1] we have;

\(73.7 = 15 \cdot 9.8 \cdot h\)

⇒\(73.7 = 147h\)

Divide both sides by 147 we get;

⇒\(h \approx 0.5\) m

Therefore,  height would the gravitational potential energy have a value of 73.7 joules for a 15 kilogram object is, 0.5 m

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