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Amanda [17]
3 years ago
14

One of the games at a carnival involves trying to ring a bell with a ball by hitting a lever that propels the ball into the air.

The height of the ball is modeled by the equation h(t)= -16t^2+39t. if the bell is 25ft above the ground, will it be hit by the ball?
Physics
1 answer:
RoseWind [281]3 years ago
8 0

Answer:

Ball will not hit bell.

Explanation:

The height of the ball is modeled by the equation h(t)= -16t²+39t

We need to find if the bell is 25 ft above the ground, will it be hit by the ball.

So we need to find maximum height of the ball.

For maximum height we have

                   \frac{dh}{dt}=0\\\\\frac{d}{dt}\left ( -16t^2+39t\right )=0\\\\-32t+39=0\\\\t=1.22s

Substituting in h(t) = -16t²+39t

Maximum height reached = h(1.22) = -16 x 1.22²+39 x 1.22 = 23.77 ft

So maximum height reached is less than height of bell.

Ball will not hit bell.

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Kiran drove from City A to City B, a distance of 228 mi. She increased her speed by 12 mi/h for the 400-mi trip from City B to C
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Answer:

From city A to city B her speed was 38 mi/h

Explanation:

The traveled distance can be calculated using this equation:

From city A to city B

228 mi = v · t₁

Where:

v = velocity

t₁ = time it took Kiran to travel the 228 mi from city A to city B

From city B to city C

400 mi = (v + 12 mi/h) · t₂

We also know that the entire trip took 14 h, then:

t₁ + t₂ = 14 h

So, we have a system of three equations with three unknwons:

228 mi = v · t₁

400 mi = (v + 12 mi/h) · t₂

t₁ + t₂ = 14 h

Let´s solve the third equation for t₁:

t₁ = 14 h - t₂

Now let´s replace t₁ in the first equation and solve it for t₂

228 mi = v · t₁

228 mi = v · (14 h - t₂)

228 mi/v - 14 h =  - t₂

t₂ = 14 h - 228 mi/v

Now let´s replace t₂ in the second equation:

400 mi = (v + 12 mi/h) · t₂

400 mi = (v + 12 mi/h) · (14 h - 228 mi/v)

400 mi = 14 h · v - 228 mi + 168 mi - 2736 mi²/(v · h)

400 mi = 14 h · v - 60 mi - 2736 mi²/(v · h)

460 mi = 14 h · v - 2736 mi²/(v · h)

Multiplicate by v both sides of the equation:

460 mi · v = 14 h · v² - 2736 mi²/h

0 = 14 h · v² - 460 mi · v - 2737 mi²/h

Solving the quadratic equation:

v = 38 mi/h

(The other solution of the equation is negative, and therefore discarded)

From city A to city B her speed was 38 mi/h

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3 years ago
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