Two cyclists set off at the same time from a point o .Cyclist p head east with a velocity of 20km/hr. Cyclist Q heads with a velocity of 16km/h .After 45 min they both stop calculate
a) the distance they have each travelled in 45 min .
b) the distance ox after 45min
c) the distance between P & Q when they both stop.
distance covered by P: 20(45/60) km = 15 km
distance covered by Q: 16(45.60) = 12 km
b) ox ? where does x come in?
c) what is 15+12 ?
To solve this problem, we'll break it down step by step:
a) To calculate the distance each cyclist has traveled in 45 minutes, we first need to convert their velocities to a common unit. Let's convert them both to km/min.
The velocity of cyclist P is given as 20 km/hr. To convert it to km/min, divide by 60 since there are 60 minutes in an hour:
Velocity of P = 20 km/hr ÷ 60 min/hr = 1/3 km/min
Similarly, the velocity of cyclist Q is given as 16 km/h. Converting it to km/min, we get:
Velocity of Q = 16 km/hr ÷ 60 min/hr = 4/15 km/min
Now, to calculate the distance traveled by each cyclist, we multiply their velocity by the time, which gives:
Distance traveled by P = Velocity of P × Time = (1/3) km/min × 45 min = 15/3 km = 5 km
Distance traveled by Q = Velocity of Q × Time = (4/15) km/min × 45 min = 12 km
Therefore, cyclist P has traveled 5 km in 45 minutes, and cyclist Q has traveled 12 km in the same time.
b) To find the distance Ox after 45 minutes, we need to find the total distance traveled in the x-direction. Since cyclist P is moving east, and the x-direction is typically considered to be the east-west direction, cyclist P's distance traveled in the x-direction is equal to the distance traveled by cyclist P.
So, the distance Ox after 45 minutes is 5 km.
c) To find the distance between point P and Q when they both stop, we need to find the distance traveled by cyclist Q in the y-direction. Since cyclist Q is moving in a different direction, we need to calculate the perpendicular distance between their positions at the end.
Since cyclist P is moving in the x-direction and cyclist Q is moving in the y-direction when they stop, we have a right-angled triangle formed between point O, P, and Q.
Using Pythagoras' theorem, we have:
Distance between P and Q = √(Distance traveled by P)^2 + (Distance traveled by Q)^2
= √(5^2 + 12^2)
= √(25 + 144)
= √169
= 13 km
So, the distance between P and Q when they both stop is 13 km.