A driveway rises 6 m over a 10 m run. Enter its climb angle in degrees, to the nearest degree. Answers within 1° are accepted.
The perpendicular pair from the Pythagoras lesson: 6 m/s east and 8 m/s north made a 10 m/s resultant. That settles the magnitude. But a resultant is a vector, so it also needs a direction.
What angle does the resultant make with east?
The two perpendicular vectors and their resultant form a right triangle, with the resultant as the hypotenuse. Mark the angle at the resultant's tail, between the eastward vector and the resultant.
The northward 8 m/s sits across from that angle: it is the opposite side. The eastward 6 m/s touches the angle and is not the longest: it is the adjacent side. So tan θ = opp / adj = 8 / 6 ≈ 1.33. And θ = tan⁻¹(8 / 6) ≈ 53°.
State the direction against its reference: the resultant points 53° north of east. Report the resultant in full: 10 m/s, 53° north of east.
A robot drives 24 m east, then 10 m north. Calculate the direction of its resultant displacement, as an angle north of east, to the nearest degree.
Write down the values in the question:
opp = 10 m (north), adj = 24 m (east), θ = ?
Write down the equation:
θ = tan⁻¹(opp / adj)
Substitute in the values:
θ = tan⁻¹(10 / 24) = tan⁻¹(0.417)
θ ≈ 23°: the resultant points 23° north of east.
Two perpendicular displacements: 20 m east and 11 m north. Enter the resultant's angle north of east, to the nearest degree. Answers within 1° are accepted.
Two perpendicular velocities act on a glider: 9 m/s east and 21 m/s north. Calculate the resultant's direction as an angle north of east, to the nearest degree.
Write down the values in the question:
opp = 21 m/s (north), adj = 9 m/s (east), θ = ?
Write down the equation:
θ = tan⁻¹(opp / adj)
Substitute in the values:
θ = tan⁻¹(21 / 9) = tan⁻¹(2.33)
θ ≈ 67°: the resultant points 67° north of east.
Two perpendicular velocities: 7 m/s east and 18 m/s north. Enter the resultant's angle north of east, to the nearest degree. Answers within 1° are accepted.
A resultant combines 12 m east and 31 m north. Which calculation gives its angle north of east?
Two perpendicular velocities act on a boat: 16 m/s east and 30 m/s north. Enter the resultant's angle north of east, to the nearest degree. Answers within 1° are accepted.
A rover drives 45 m east, then 24 m north. Enter the direction of its resultant displacement as an angle north of east, to the nearest degree. Answers within 1° are accepted.
Two perpendicular velocities: 14 m/s west and 25 m/s north. Enter the resultant's angle north of west, to the nearest degree. Answers within 1° are accepted.