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kramer
3 years ago
14

A quarterback throws a football with an initial velocity v at an angle θ above horizontal. Assume the ball leaves the quarterbac

k’s hand at ground level and moves without air resistance. All portions of this problem will produce algebraic expressions in terms of v, θ, and g. Let the origin of the Cartesian coordinate system be the ballʼs initial position.
(a): Write an expression for the magnitude of the football’s initial vertical velocity v0y.
(b): Find an expression for the magnitude of the football’s initial horizontal velocity v0x.
Physics
1 answer:
Maru [420]3 years ago
6 0
(a) The y-component or vertical velocity is calculated using:
Vy = Vsin(∅)

(b) The x-component or horizontal velocity is calculated using:
Vx = Vcos(∅)
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A boat traveling across a river has a resultant velocity of 10 km/h and travels 34 degrees with respect to the shore. A) What is
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a) 1.55 m/s

b) 2.3 m/s

Explanation:

We know that the boat travels across the river, if we define the river as the x-axis, then the velocity of the boat is only on the y-axis.

Then we can write the velocity of the boat in still water as:

S = (0, B)

Now, when the boat is on the river, the velocity of the boat will be equal to the velocity of the boat in still water plus the velocity of the river.

The velocity of the river is:

v = (R, 0).

Then the velocity of the boat in that river is:

V' = (0, B) + (R, 0) = (R, B)

Now, we know that the velocity of the boat is 10km/h, and it travels at an angle of 34° with respect to the shore.

We can use the Pythagoreans theorem to write the components of this velocity as:

x-axis component = 10km/h*cos(34°) = 8.29 km/h

y-axis component = 10km/h*sin(34°) =  5.59 km/h

Then the velocity of the boat can be written in components as:

velocity = ( 8.29 km/h,  5.59 km/h)

And we knew that the velocity of the boat was written as  (R, B)

Then we must have:

R = 8.29 km/h

B = 5.59 km/h

a) The speed of the boat in m/s:

We know that the speed of the boat is 5.59 km/h.

First, we know that:

1km = 1000m, then:

5.59 km/h = 5.59*(1000m)h = 5,590 m/h

And we know that:

1h = 3600s

Then we can write:

5,590 m/h = 5,590 m/(3600s) = 1.55 m/s

b) The speed of the river in m/s:

We know that the speed of the river is 8.29 km/h

Using the same reasoning as above, we can do the change of units as follows:

8.29 km/h = 8.29 (1000m)/(3600s) = 2.3 m/s

6 0
3 years ago
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