1. A stone is thrown vertically upward with a speed of 16.0 m/s. A. How fast is

Question

1. A stone is thrown vertically upward with a speed of 16.0 m/s.

A. How fast is it moving when it reaches a height of 11 m?

B. How long is required to reach this height?

C. Why are there two answers to part B?

2. You are driving home from school steadily at 97km/h for 150km . It then begins to rain and you slow to 61km/h . You arrive home after driving 3 hours and 30 minutes.

a. How far is your hometown from school?

b. What was your average speed?

3. A diver running 2.7m/s dives out horizontally from the edge of a vertical cliff and 2.6s later reaches the water below.

A. How high was the cliff?

B. How far from its base did the diver hit the water?

4. A projectile is fired with an initial speed of 69.3m/s at an angle of 39.6? above the horizontal on a long flat firing range.

a. Determine the maximum height reached by the projectile.

b. Determine the total time in the air.

c. Determine the total horizontal distance covered (that is, the range).

d. Determine the speed of the projectile 1.74s after firing.

e. Determine the direction of the projectile 1.74s after firing.

5. A batter hits a fly ball which leaves the bat 0.85mabove the ground at an angle of 61? with an initial speed of 28m/s heading toward centerfield. Ignore air resistance.

a. How far from home plate would the ball land if not caught?

b.The ball is caught by the centerfielder who, starting at a distance of 105m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level. Find his speed.

Explanation / Answer

1) a) v^2 = u^2 -2gh

v = sqrt(16^2 - (2*9.8*11)) = 6.356 m/s

b) time t = u/g = 16/9.8 = 1.6326 s

2) time taken for 150 kmbe t1

t1 = 150/97=1.5464 hrs

remaining time t2 = 3.5-1.5464 = 1.953 hrs

distance travelled at 61km/h = 61*1.953 = 119.1 km

total distance = 150+119.17 = 269.17 km

b) av speed = total distance/total time

Vav = 269.17/3.5 = 76.9 km/h

3) H = 0.5gt^2

H = 0.5*9.8*2.6^2

H = 33.124 m

R = v*t = 2.7*2.6 = 7.02 m

4) a) Hmax = u^2sin(tehta)^2/2g

Hmax = 69.3^2*sin39.6^2/2*9.8 = 99.556 m

b) total time in air = 2usin(teta)/g

total time = 2*69.3*sin39.6/9.8 = 9.015 s

c) R = ucos(tehta)*t = 69.3*cos39.6*9.015 = 481.37 m

d) vertical component of velocity be Vy

Vy^2 = Uy - gt

Vy = 69.3*sin39.6 - 9.8*1.74 = 27.12 m/s

Vx = 69.3cos39.6 = 53.396 m/s

V = sqrt(Vx^2 +Vy^2) = 59.89 m/s

e) direction theta = arctan(Vy/Vx) = arctan(27.12/53.396) = 26.926 degrees

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