I've been having a bit of trouble with these questions, my exam is coming up soon and all help would greatly be appreciated.
Q1.
A dancer in a school musical is asked to leap 80 cm into the air, taking off vertically on one beat of the music and landing with the next beat. If the music beats every 0.5 seconds, is the leap possible? The acceleration of the dancer during the leap can be assumed to be 10 ms^-2 downwards.
Q2.
A brand-new Rolls Royce rolls off the back of a truck as it is being delivered to its owner. The truck is traveling along a straight road at a constant speed of 60 km^-1. The rolls Royce slows down at a constant rate, coming to a stop over a distance of 240 m. It is a full minute before the truck driver realizes that the precious load is missing. The driver brakes immediately, leaving a 25 m long skid mark on the road. The driver's reaction time is 0.5 s. How far is the Rolls Royce when the truck stops?
Please show your working, as this would help me greatly. Thank you everyone for your time.
Q1.
A dancer in a school musical is asked to leap 80 cm into the air, taking off vertically on one beat of the music and landing with the next beat. If the music beats every 0.5 seconds, is the leap possible? The acceleration of the dancer during the leap can be assumed to be 10 ms^-2 downwards.
Q2.
A brand-new Rolls Royce rolls off the back of a truck as it is being delivered to its owner. The truck is traveling along a straight road at a constant speed of 60 km^-1. The rolls Royce slows down at a constant rate, coming to a stop over a distance of 240 m. It is a full minute before the truck driver realizes that the precious load is missing. The driver brakes immediately, leaving a 25 m long skid mark on the road. The driver's reaction time is 0.5 s. How far is the Rolls Royce when the truck stops?
Please show your working, as this would help me greatly. Thank you everyone for your time.
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Q1. The dancer must leap up and back down during a time interval of 0.5
Time to leap Up = 0.25 s
S = 0.8 = Vo t = 1/2 g t^2 = 0.25 Vo - 4.9 (0.25)^2 and Vo = 4.424 m/s
IS IT POSSIBLE? Maybe, but not likely for a human to jump something like 14.6 ft in the air in one second.
Q2.
Initial velocity of the car is the same as that of the truck 60km/hr x 1000m/km x 1 hr/3600 s = 16.67 m/s
The car comes to a full stop over a distance of 240 m
Vf^2 - Vo^2 = 2 a S
0 - (16.67)^2 = 2 a (240 and a = - 0.579 m/s^2
The time it takes the car to stop = t
S = Vo t - 1/2 a t^2
240 = 16.67 t - 4.9 t^2
Solve the quadratic equation to get t=30.16 s
This step may not be required..
The distance between the car and the truck = 240 m + the time travelled by the truck during 65 seconds + 25 m Skid
= 240 + (16.67 x 65 + 25 = 1348.55 m
Time to leap Up = 0.25 s
S = 0.8 = Vo t = 1/2 g t^2 = 0.25 Vo - 4.9 (0.25)^2 and Vo = 4.424 m/s
IS IT POSSIBLE? Maybe, but not likely for a human to jump something like 14.6 ft in the air in one second.
Q2.
Initial velocity of the car is the same as that of the truck 60km/hr x 1000m/km x 1 hr/3600 s = 16.67 m/s
The car comes to a full stop over a distance of 240 m
Vf^2 - Vo^2 = 2 a S
0 - (16.67)^2 = 2 a (240 and a = - 0.579 m/s^2
The time it takes the car to stop = t
S = Vo t - 1/2 a t^2
240 = 16.67 t - 4.9 t^2
Solve the quadratic equation to get t=30.16 s
This step may not be required..
The distance between the car and the truck = 240 m + the time travelled by the truck during 65 seconds + 25 m Skid
= 240 + (16.67 x 65 + 25 = 1348.55 m