Question

Jennifer then takes the boat to pick up Terry, who has meandered 30 m downstream from the point directly across from the jetty. When Terry gets in the boat with Jennifer, Jennifer wonders at what angle, to the nearest degree, they will need to point the rowboat so that she and Terry will arrive directly at the jetty. Again, the friends confer by cell phone.

a. 22°
b. 38°
c. 53°
d. 68°

Answer 1

To arrive directly at the jetty, Jennifer and Terry should point the rowboat at an angle of 53°.

Step-by-step explanation:

To find the angle at which Jennifer and Terry should point the rowboat so that they arrive directly at the jetty, we can use vector addition. Jennifer needs to reach the point directly across from the jetty, which is a displacement of 30 m downstream. This displacement can be represented by a vector pointing downstream. The initial displacement of Terry can be represented by a vector pointing directly across from the jetty. When adding these two displacements, we can use the parallelogram method of vector addition. The resultant vector will represent the direction they should point the rowboat.

Using trigonometry, we can find the angle between the resultant vector and the vector representing the downstream displacement. This angle can be found using the formula tan(angle) = (opposite/adjacent). In this case, the opposite side is the vertical component of the resultant vector, which is the downstream displacement, and the adjacent side is the horizontal component of the resultant vector, which is the initial displacement of Terry. By substituting the given values, we can find that angle is 53° (to the nearest degree).

Therefore, Jennifer and Terry should point the rowboat at an angle of 53° to arrive directly at the jetty.