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1 month ago

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Emily throws a soccer ball out of her dorm window to Allison, who is waiting below to catch it. If Emily throws the ball at an a

ngle of 30º below the horizontal with a speed of 14m/s, how far from the base of the dorm should Allison stand to catch the ball? Assume the vertical distance between where Emily releases the ball and Allison catches it is 8.0m.

2 answers:

Yuliya22 [3.3K]1 month ago

8 0

Solution:

6.778 meters

Step-by-step:

Using the equation of motion: y = u t + ½ a t²

6 m = (initial velocity component) + (½ acceleration × time squared)

6 = 12 × sin 30° × t + ½ × 9.81 × t²

This leads to the quadratic equation: 4.905 t² + 6 t - 6 = 0

Solving, we find t = 0.6522 seconds.

Calculating horizontal distance:

x = (initial speed) × cos 30° × t

= 12 × cos 30° × 0.6522

= 6.778 meters

Sav [3.1K]1 month ago

7 0

Result:

d = 9.1 meters

Explanation:

The ball’s initial speed is given as

$v_i = 14 m/s$

Since it is thrown 30 degrees below the horizontal,

we use trigonometric components:

$v_x = 14 cos 30$

$v_x = 12.12 m/s$

$v_y = 14 sin30$

$v_y = 7 m/s$

For the vertical displacement: the ball falls 8.0 m

The acceleration in the vertical direction is due to gravity

Hence,

$\Delta y = v_y t + \frac{1}{2}gt^2$

$8 = 7 t + \frac{1}{2}(9.81)t^2$

$t = 0.75 s$

The horizontal distance covered during this time is

$d = v t$

$d = 12.12 \times 0.75$

$d = 9.1 m$

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A particular brand of gasoline has a density of 0.737 g/mLg/mL at 25 ∘C∘C. How many grams of this gasoline would fill a 14.9 gal

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Answer:

The answer to your inquiry is Mass = 41230.7 g or 41.23 kg.

Explanation:

Data

Density = 0.737 g/ml

Mass = ?

Volume = 14.9 gal

1 gal = 3.78 l

Process

1.- Convert gallons to liters

1 gal ---------------- 3.78 l

14.9 gal ------------- x

x = 56.44 l

2.- Convert liters to milliliters

1 l ------------------- 1000 ml

56.44 l --------------- x

x = (56.44 x 1000) / 1

x = 56444 ml

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Formula

Density = $\frac{mass}{volume}$

Solving for mass

Mass = density x volume

Substituting values

Mass = 0.737 x 56444

Result

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