Answer:
1. Mary has 20 joules of Kinetic energy
2. Yes his kinetic energy be twice as much
3. If Roberto runs twice as fast, his Kinetic energy will be 4 times as much
4. 16875 Joules
5. 5.77 m/s
6. 8 kg
7. 345600 J
Explanation:
The formula for Kinetic Energy is given as [tex]KE= 0.5\times m \times v^{2}[/tex]
We will apply this in solving all the problems below using the parameters provided by each problem.
1. Mary's Kinetic Energy will be equal to [tex]0.5 \times 40 \times 1^{2}=20joules[/tex]
2a. If Roberto has twice Mary's mass, his mass will be 80 kg.
His K.E will be [tex]KE= 0.5\times 80 \times 1^{2}= 40 joules[/tex]
2b. If Roberto runs twice as fast, his kinetic energy will be [tex]KE= 0.5\times 80 \times 2^{2}= 160 joules[/tex]. This is four times its initial value
4. [tex]KE= 0.5\times 150 \times 15^{2}= 16875 joules[/tex]
5. [tex]v=\sqrt{\frac{500}{0.5 \times 30}}=5.77m/s[/tex]
6. [tex]mass, m = \frac{100}{0.5 \times 5^{2}}= 8kg[/tex]
7. [tex]KE= 0.5\times 1200 \times 24^{2}= 345600 joules[/tex]
