Question

A cyclist moving with a speed of 8 m/s has a kinetic energy of 1500 J. What is

the mass of the cyclist?​

Answer 1

Given :

• Speed of the cyclist is 8 m/s
• Kinetic energy of the cyclist = 1500 J

To find :

• The mass of the cyclist

Solution :

The relation between mass , kinetic wnergy and velocity is given by ,

$\boxed {\rm{KE = \frac{1}{2}M {V}^{2} }}$

We have ,

• v = 8 m/s
• KE = 1500 J
• m = ?

By substituting the values ,

$: \implies \rm \: 1500 \: J= \frac{1}{2} \times M \times (8 \: m {s}^{ - 1} ) {}^{2} \\ \\ : \implies \rm \: 1500 \: J= \frac{1}{2} \times M \times 64 \: m {}^{2} {s}^{ - 2 } \\ \\ : \implies \rm \: 1500 \: kgm {}^{2} {s}^{ - 2} = 32 m {}^{2} {s}^{ - 2} \times M \\ \\ : \implies \rm \: 1500 \: kg \: \cancel{ {m}^{2} {s}^{ - 2} } = 32 \: \cancel{ {m}^{2} {s}^{ - 2} } \times M\\ \\ : \implies \rm \: 1500 \: kg = 32M \\ \\ : \implies \rm \: \frac{1500 \: kg}{32} = M \\ \\ : \implies \rm \: M = 46.87 \: kg$

∴ The mass of the cyclist is 46.87 kg

Answer 2

Answer:

Given :

Speed of the cyclist is 8 m/s

Kinetic energy of the cyclist = 1500 J

To find :

The mass of the cyclist

Solution :

The relation between mass , kinetic wnergy and velocity is given by ,

\boxed {\rm{KE = \frac{1}{2}M {V}^{2} }}

KE=

2

1

MV

2

We have ,

v = 8 m/s

KE = 1500 J

m = ?

By substituting the values ,

\begin{gathered} : \implies \rm \: 1500 \: J= \frac{1}{2} \times M \times (8 \: m {s}^{ - 1} ) {}^{2} \\ \\ : \implies \rm \: 1500 \: J= \frac{1}{2} \times M \times 64 \: m {}^{2} {s}^{ - 2 } \\ \\ : \implies \rm \: 1500 \: kgm {}^{2} {s}^{ - 2} = 32 m {}^{2} {s}^{ - 2} \times M \\ \\ : \implies \rm \: 1500 \: kg \: \cancel{ {m}^{2} {s}^{ - 2} } = 32 \: \cancel{ {m}^{2} {s}^{ - 2} } \times M\\ \\ : \implies \rm \: 1500 \: kg = 32M \\ \\ : \implies \rm \: \frac{1500 \: kg}{32} = M \\ \\ : \implies \rm \: M = 46.87 \: kg\end{gathered}

:⟹1500J=

2

1

×M×(8ms

−1

)

2

:⟹1500J=

2

1

×M×64m

2

s

−2

:⟹1500kgm

2

s

−2

=32m

2

s

−2

×M

:⟹1500kg

m

2

s

−2

=32

m

2

s

−2

×M

:⟹1500kg=32M

:⟹

32

1500kg

=M

:⟹M=46.87kg

∴ The mass of the cyclist is 46.87 kg