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avanturin [10]
3 years ago
14

A father lifts a toddler 1.5 m up in the air. The child gains 187.5 J of energy in her gravitational potential energy store as a

result. What is the mass of the toddler? Give your answer to 1 decimal place. (Assume that the gravitational field strength is 10 N/kg.)
Mathematics
1 answer:
professor190 [17]3 years ago
8 0

The mass of the toddler is 12.5 kg

Step-by-step explanation:

Gravitational potential energy (GPE) =

mass (m) × height (h) × gravitational field strength (g)

1. Gravitational potential energy is measured in (J)

2. Mass is measured in (kg)

3. Height is measured in (m)

4. Gravitational field strength (g) is measured in (N/kg)

∵ A father lifts a toddler 1.5 m up in the air

∴ h = 1.5 m

∵ The child gains 187.5 J of energy in her gravitational potential

   energy store as a result

∴ GPE = 187.5 j

- Assume that the gravitational field strength is 10 N/kg

∴ g = 10 N/kg

Substitute the values of GPE , h and g in the rule above to find m

∵ GPE = m h g

∴ 187.5 = m × 1.5 × 10

∴ 187.5 = 15 m

- Divide both sides by 15

∴ m = 12.5 kg

The mass of the toddler is 12.5 kg

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6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the
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Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

a_1 the horizontal distance between the first observer and the ballonist

a_2 the horizontal distance between the second observer and the ballonist

\alpha _1 and \alpha _2 the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

S=a*h (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

S=S_1+S_2 (equation 2)

S_1=a_1*h

But we can write S_1 in terms of \alpha _1, like this:

\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}

And for S_2 will be the same:

S_2=\frac{h^{2} }{\tan(\alpha _2)}

Replacing in the equation 2:

S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})

And replacing in the equation 1:

h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}

So, we can replace all the known data in the last equation:

h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

6 0
3 years ago
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