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pantera1 [17]
2 years ago
6

A baseball is hit when it is 2.5 ft above the ground. It leaves the bat with an initial velocity of 145 ft/sec at a launch angle

of 23°. At the instant the ball is hit, an instantaneous gust of wind blows against the ball, adding a component of -14i (ft/sec) to the ball’s initial velocity. A 15-ft-high fence lies 300 ft from home plate in the direction of the flight.
a. Find a vector equation for the path of the baseball.
b. How high does the baseball go, and when does it reach maxi-mum height?
c. Find the range and flight time of the baseball, assuming that the ball is not caught.
d. When is the baseball 20 ft high? How far (ground distance) is the baseball from home plate at that height?
e. Has the batter hit a home run? Explain.
Physics
1 answer:
sergiy2304 [10]2 years ago
8 0

Answer:

Explanation:

Take base of the ground as origin .

component of initial velocity along i and j direction is 145 con23 and 145 sin23 . Along j , gravity acts but along i , no force acts .  

The path  of ball in vector form

s = (145 cos23- 14 )t  i + ( 2.5 + 145sin23 t - 1/2 g t² ) j

t is time period .

b )

vertical component of initial velocity = 145 sin 23 =

for vertical displacement

v² = u² - 2gH

For maximum height , v = 0

0 = (145 sin 23 )² - 2 g H , H is maximum height attained .

H = 3209.56 / 2 x 9.8

= 163.75 m

Total height attained = 163.75 + 2.5 = 166.25 m

if time be t for reaching maximum height

v = u -gt

0 = 145 sin 23 - gt

t = 145 sin23 / g

= 5.78 s

c )

For time of flight , vertical displacement = 2.5 m

2.5 = - 145 sin 23 t + 1/2 g t²

2.5 = -56.65 t + 4.9 t²

4.9 t² - 56.65 t - 2.5 = 0

t = 11.60s

horizontal displacement during this period = 145 cos23 x 11.60 = 1548.28 m

Range = 1548.28 m.

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You are designing a delivery ramp for crates containing exercise equipment. The 1470-N crates will move at 1.8 m/s at the top of
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Answer:

The force constant ,I = 2394N/m

Explanation:

Given:

Weight of crate,Wg = 1470N

Theta = 22.0°

Kinetic friction,Fk= Fs(max) = 550N

Total length of ramp =8.0m

If y =0 at the bottom of the ramp

y1 = d Sin theta

y1 = 8 × Sin 22°

y1 = 3.0m

y2 = 0

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V2 = 0

The equation combining the gravitational and elastic potential energy, and the work energy theorem is given by:

K1 + Ugrav1 + Uel1 + W = K2 + Uel1 ..eq1

Where KE is given by: 1/2mv^2

Gravitational potential energy is given by: Ugrav = mgy ...eq2

Elastic potential energy = Uel = 1/2Kx^2 ..eq3

The restoring force constant of a spring compressed by a distance x is given by:

Fx = Kx ..eq4

Workdone by a constant force is given by W = Fscostheta ...eq5

Where s = displacement

Theta = the angle between the force and the displacement

Work,W = Wf = 550 ×8 × cos 180°

W = -4400J

From the weight of the crate.mass is:

Wg/g = m

1470/9.8 = 150kg

K1 = 1/2 ×150×1.8^2 = 243m/s

The crate comes to rest at K2=0

Ugrav1 = 150 × 9.8 × 3 = 4410J

Ugrav2 = 150 × 9.8 x 0 = 0J

Uel1= 0 Spring at equilibrium

Substituting the values of the energies and work

253 + 4410 + 0 - 4400 = 0 + 0 + Uel1

Uel1 = 253J

Substituting into eq3

253 = 1/2 Kx^2 = 1/2 Kx(x)

Kx = 506/x

Since crate remains at rest,we use Newton's 2nd law

Fx = fs + Wsin theta

Fx = 550 + 1470 sin 22

Fx = 1100.7N

Substituting into eq4

Kx = 1100.7

X = 506/1100.7 = 0.46m

Kx = 1100.7

K = 1100.7/0.47

K = 2394N/m

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