Question

Dina goes to a carnival. The rides with a height requirement cost 3 tickets, and the rides without a height requirement cost 4 tickets. Dina is tall enough to go on all the rides. She has 24 tickets in total.

How many of each type of ride can Dina go on using all 24 tickets?

A. 6 tall rides, 0 short rides
B. 5 tall rides, 3 short rides
C. 4 tall rides, 6 short rides
D. 3 tall rides, 9 short rides

Answer 1

The requirement is to calculate the centripetal force needed for Dina to remain on a merry-go-round at a given rotational speed and a specific radius from the center. The rotational speed needs to be converted from rev/min to rad/s before it can be entered into the centripetal force formula.

Step-by-step explanation:

The student is attempting to calculate the centripetal force required for Dina to stay on a merry-go-round. To find this, we must first convert the rotation speed from revolutions per minute (rev/min) to radians per second (rad/s), and then apply the formula for centripetal force, which is F = mv2/r.

First, convert the rotational speed to radians per second:

• Convert revolutions per minute to revolutions per second: 3 rev/min ÷ 60 = 0.05 rev/s
• Since 1 revolution is 2π radians, multiply 0.05 rev/s by 2π to get the angular velocity in rad/s.

Now, we can apply the formula. Assuming we know Dina's mass (m), and given that the radius of the merry-go-round (r) is 8.00 m, the linear velocity (v) can be found using v = rω where ω is the angular velocity. With these values, we can plug them into the centripetal force formula to find the necessary force.