A car travels 2.72 km in the x-direction, then
turns left 68 degrees to the original direction and
travels an additional distance of 3.2 km.
Calculate the x component of the car's net
displacement. Answer in units of km.
2007-08-12 16:15:49 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Physics
Be sure you are differentiating the equation properly, and do so BEFORE you take the limit.
2007-08-12 16:28:58 · answer #1 · answered by Anonymous · 1⤊ 1⤋
You need to figure out the x component of the cars direction after it turns 68 degrees to the left. Assuming that it is traveling in the positive x-direction (it doesn't really matter in the end), you can use the cosine function to figure out the x component. The cos of an angle is equal to the adjacent side of the angle divided by the hypotenuse. In this case your hypotenuse is 3.2 km (the direction the car is traveling), the angle is 68 degrees. Thus
cos 68 = x/3.2
.375 = x/3.2
x = 1.2
Thus add this extra x-distance to the original x-displacement of 2.72 to get 3.92 km.
2007-08-12 23:37:38 · answer #2 · answered by Stevie B 3 · 1⤊ 0⤋
Draw arrows to trace the path of the car. You should have an obtuse triangle. Now, extend the line horizontally at the turn and vertically at the destination. You should have a right triangle. The angles of the right triangle are 60, 22, and 90.
sin22 = x/3.2 ---> x = 1.2 km
But remember that the car travelled 2.72 km before turning.
2.72 + 1.2 = 3.92 km
2007-08-12 23:39:55 · answer #3 · answered by Philippe 3 · 0⤊ 1⤋
This is simple trig.
You've got two angles & a side.....
2007-08-12 23:35:34 · answer #4 · answered by Irv S 7 · 0⤊ 1⤋