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Lady bird [3.3K]
3 years ago
13

A hot air balloon is rising vertically with a velocity of 10.0 feet per second. A very small ball is released from the hot air b

alloon at the instant when it is 960 feet above the ground. Use a(t)=−32 ft/sec2 as the acceleration due to gravity.
1. How many seconds after its release will the ball strike the ground? Round the answer to the nearest two decimal places.

2. At what velocity will it hit the ground?
Physics
1 answer:
krek1111 [17]3 years ago
7 0

Answer:

Explanation:

Given that,

The rising velocity of the balloon

U = 10 ft/s

The height where a small balloon is release is

y = 960ft

Taking g = - 32 ft/s²

A. Time the balloon will strike the ground.

Using the equation of free fall

∆y = ut + ½gt².

0—960 = 10t + ½× -32 × t²

- 960 = 10t —16t²

16t² — 10t — 960 = 0

Divide through by 2

8t²—5t —480= 0

Using quadratic formula method

t = [-b ± √(b²-4ac)] / 2a

a = 8 b = -5 and c = -480

t = [--5 ± √((-5)²-4×8×-480)] / 2×8

t = [5 ± √(25+15360)] / 16

t = [5 ± 124.04] / 16

Let discard the negative time since time can't be negate

Then, t = [5+124.06] / 16

t = 8.065 seconds

To 2d.p

t = 8.06 seconds

B. Final velocity it hits the ground

Using equation of motion.

V = U + gt

V = 10 + (-32) × 8.06

V = 10 — 258.07

V = —248.07m/s

The negative sign is showing that it is moving downward

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2 years ago
7. A mother pushes her 9.5 kg baby in her 5kg baby carriage over the grass with a force of 110N @ an angle
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Weight of the carriage =(m+M)g =142.1\ N

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Explanation:

We have to look into the FBD of the carriage.

Horizontal forces and Vertical forces separately.

To calculate Weight we know that both the mass of the baby and the carriage will be added.

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To calculate normal force we have to look upon the vertical component of forces, as Normal force is acting vertically.We have weight which is a downward force along with F_x, force of 110\ N acting vertically downward.Both are downward and Normal is upward so Normal force =Summation\ of\ both\ forces

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To calculate acceleration we will use Newtons second law.

That is Force is product of mass and acceleration.

We can see in the diagram that F_y=Horizontal and F_x=Vertical component of forces.

So Fnet = Fy(Horizontal) - f(friction) = m\times a

  • Acceleration (a) =\frac{Fcos(\theta)-\mu N}{mass(m)} =\frac{(95.26-27.59)}{14.5}= 4.66\ m\ s{^2 }

So we have the weight of the carriage, normal force,frictional force and acceleration.

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