This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Question 9: To find the resultant of two vectors by calculation, use the formula: R = sqrt(V_1^2 + V_2^2 + 2V_1V_2 ) where V_1 = 3 units, V_2 = 4 units, and is the angle between them. Note: The "by drawing" part cannot be performed by an AI. a) Inclined at 30^ Step 1: Substitute the values into the formula. R &= sqrt((3 units))^2 + (4 units)^2 + 2(3 units)(4 units) (30^) \\ &= sqrt(9 units)^2 + 16 units^2 + 24 units^2 (sqrt(3)2) \\ &= sqrt(25 units)^2 + 12sqrt(3) units^2 \\ &= sqrt(25 + 12 × 1.73205) units \\ &= sqrt(25 + 20.7846) units \\ &= sqrt(45.7846) units \\ &≈ 6.77 units The resultant is 6.77 units. b) Inclined at 90^ Step 1: Substitute the values into the formula. R &= sqrt((3 units))^2 + (4 units)^2 + 2(3 units)(4 units) (90^) \\ &= sqrt(9 units)^2 + 16 units^2 + 24 units^2 (0) \\ &= sqrt(25 units)^2 \\ &= 5 units The resultant is 5 units. c) Inclined at 120^ Step 1: Substitute the values into the formula. R &= sqrt((3 units))^2 + (4 units)^2 + 2(3 units)(4 units) (120^) \\ &= sqrt(9 units)^2 + 16 units^2 + 24 units^2 (-(1)/(2)) \\ &= sqrt(25 units)^2 - 12 units^2 \\ &= sqrt(13 units)^2 \\ &≈ 3.61 units The resultant is 3.61 units. Question 10: A component of a vector is its effective value along a specific direction, obtained by projecting the vector onto that direction. For a vector A at an angle to the horizontal, its horizontal component is A_x = A and its vertical component is A_y = A . Illustration with a diagram: Imagine a vector originating from the origin of a Cartesian coordinate system. Its horizontal component is the projection onto the x-axis, and its vertical component is the projection onto the y-axis, forming a right-angled triangle with the vector as the hypotenuse. Calculation of components: Given force F = 150 N, inclined at = 50^ to the horizontal. Step 1: Calculate the horizontal component (F_x). F_x = F = 150 N × (50^) F_x ≈ 150 N × 0.6428 F_x ≈ 96.42 N The horizontal component is 96.42 N. Step 2: Calculate the vertical component (F_y). F_y = F = 150 N × (50^) F_y ≈ 150 N × 0.7660 F_y ≈ 114.90 N The vertical component is 114.90 N. That's 2 down. 3 left today — send the next one.