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marta [7]
3 years ago
7

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.60 m/s. The car is a distan

ce d away. The bear is 39.3 m behind the tourist and running at 5.00 m/s. The tourist reaches the car safely. What is the maximum possible value for d
Physics
1 answer:
In-s [12.5K]3 years ago
7 0

Answer:

101 meters

Explanation:

Distance traveled by the tourist:

d = 3.60 m/s × t

Distance traveled by the bear:

d + 39.3 m = 5.00 m/s × t

Substitute:

3.6 t + 39.3 = 5 t

39.3 = 1.4 t

t = 28.1

d = 101

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A thermometer initially reading 212F is placed in a room where the temperature is 70F. After 2 minutes the thermometer reads 125
frez [133]

Answer:

91.3°F

Explanation:

Let T be the temperature of the thermometer at any time

T∞ be the temperature of the room = 70°F

T₀ be the initial temperature of the thermometer = 212°F

And m, c, h are all constants from the cooling law relation

From Newton's law of cooling

Rate of Heat loss by the cake = Rate of Heat gain by the environment

- mc (d/dt)(T - T∞) = h (T - T∞)

(d/dt) (T - T∞) = dT/dt (Because T∞ is a constant)

dT/dt = (-h/mc) (T - T∞)

Let (h/mc) be k

dT/(T - T∞) = -kdt

Integrating the left hand side from T₀ to T and the right hand side from 0 to t

In [(T - T∞)/(T₀ - T∞)] = -kt

(T - T∞)/(T₀ - T∞) = e⁻ᵏᵗ

(T - T∞) = (T₀ - T∞)e⁻ᵏᵗ

Inserting the known variables

(T - 70) = (212 - 70)e⁻ᵏᵗ

(T - 70) = 142 e⁻ᵏᵗ

At t = 2 minute, T = 125°F

125 - 70 = 142 e⁻ᵏᵗ

55/142 = e⁻ᵏᵗ

- kt = In (55/142) = In (0.3873)

- k(2) = - 0.9485

k = 0.4742 /min

At time t = 4 mins

kt = 0.4742 × 4 = 1.897

(T - 70) = 142 e⁻ᵏᵗ

e^(-1.897) = 0.15

T - 70 = 142 × 0.15 = 21.3

T = 91.3°F

7 0
3 years ago
Are most plants and animals single-cell organisms
Anestetic [448]
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3 0
3 years ago
Read 2 more answers
Naoki's bicycle has a mass of 9 kg. If Naoki sits on her bicycle and starts pedaling with a force of 107.2 N, causing an acceler
Murrr4er [49]

Answer:

Explanation:

F = ma

m = F/a

m = 107.2/1.6 = 67 kg

so Naoki's mass must be the total mass - mass of the bike

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6 0
3 years ago
A roller coaster is going through a loop with a circular radius of 9.1 meters, how fast must the roller coaster be moving at the
Verdich [7]

Answer:

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Explanation:

8 0
3 years ago
A block is balanced on top of a frictionless sphere of radius R. When the block is given a slight nudge it starts to slide down
Nataly_w [17]

Answer:\frac{R}{3}

Explanation:

Given

Sphere of Radius R

Suppose mass of block is m

At any instant \theta Normal reaction(N) and weight(mg) is acting such that

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When block is just about to leave then N=0

therefore

mg\sin \theta =\frac{mv^2}{R}

v^2=gR\sin \theta-------------------1

Also by conserving Energy we get

Potential Energy=kinetic Energy of block

mgh=\frac{mv^2}{2}

here h=vertical distance traveled by block

From diagram

h=R-R\sin \theta

h=R(1-\sin \theta )

mgR(1-\sin \theta )=\frac{mv^2}{2}

2gR(1-\sin \theta )=v^2-----------------2

From 1 and  2

2(1-\sin \theta )=\sin \theta

3\sin \theta =2

\sin \theta =\frac{2}{3}

Thus from this value of h is

h=R(1-\sin \theta )

h=R(1-\frac{2}{3})

h=\frac{R}{3}

3 0
3 years ago
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