🔭 physics

1. **Problem statement:** We have an elastic band initially 20 cm long. Each increase of 1 newton in force stretches the band by 0.125 cm.

1. **Problem statement:** We have an elastic band initially 20 cm long. Each increase of 1 newton in force stretches the band by 0.125 cm.

1. **Problem Statement:** The speed of a projectile at the highest point is given as $\frac{1}{\sqrt{2}}$ times its initial speed $u$. We need to find the horizontal range of the p

1. **Problem statement:** We have two charges, +q and -q, separated by a distance of 9.0 cm, experiencing an electrostatic force of 5.0 N. We need to find the magnitude of each cha

1. **Problem Statement:** We are given the decay formula for polonium-210 (210 Po): $$A(t) = 0.7 \left(\frac{1}{2}\right)^{\frac{t}{138.4}}$$

1. **Problem statement:** We need to find the displacement vector from Winnipeg to Saskatoon given two vectors: Winnipeg to Regina (530 km at 6.9° north of west) and Regina to Sask

1. **Problem statement:** We need to find the difference between the speed of the space probe as it travels towards Venus and the speed as it travels away from Venus based on the d

1. نُعطى القوة \( \mathbf{ن} = 3\hat{\mathbf{x}} + 2\hat{\mathbf{y}} \) عند نقطة ما، ومتجه عزم \( \mathbf{ن} \) حول نقطة الأصل هو \( 15\hat{\mathbf{z}} \). 2. نريد إيجاد نقطة تقاطع

1. **Problem Statement:** Identify the diagram and analyze the energy conversions and magnitudes at points A, B, C, and D on a semicircular arc with given points.

1. **Problem 7: Find the scalar product of two vectors A and B** given $A=5.0$, $B=8.0$, and the angle $\alpha=30^\circ$ between them. 2. The scalar product (dot product) formula i

1. Problem: Find the direction of vector $\mathbf{C} = 2\mathbf{A} - \mathbf{B}$ where $\mathbf{A} = 12\mathbf{i} - 16\mathbf{j}$ and $\mathbf{B} = -24\mathbf{i} + 10\mathbf{j}$.\n

1. **Problem:** Find the direction of vector $\mathbf{C} = 2\mathbf{A} - \mathbf{B}$ where $\mathbf{A} = 12\mathbf{i} - 16\mathbf{j}$ and $\mathbf{B} = -24\mathbf{i} + 10\mathbf{j}

1. The problem is to understand the meaning and context of $g = -9.8$. 2. In physics, $g$ typically represents the acceleration due to gravity near the Earth's surface.

1. **State the problem:** A rock is thrown downward from a 40.0 m tall tower with an initial speed of 12 m/s. We need to find the speed of the rock just before it hits the ground,

1. **Problem statement:** An object is thrown vertically upward. When it reaches one fourth of its maximum height, its velocity is 18 m/s upward. We need to find the initial launch

1. The user requested a free body diagram, which is a visual representation of forces acting on an object. 2. As a text-based AI, I cannot generate images or diagrams directly.

1. **Problem Statement:** A wheel starts from rest with an angular acceleration given by $$\alpha(t) = \alpha_0 e^{-kt}$$ where $$\alpha_0 = 2.0\ \text{rad/s}^2$$ and $$k = 0.5\ \t

1. **Problem Statement:** We have a spinning disk with angular acceleration given by $\alpha(t) = -ct$, where $c = 0.2$ rad/s$^3$. The initial angular velocity is $\omega_0 = 5$ ra

1. **Problem statement:** Find the acceleration of a particle moving along the x-axis at the time when it reaches its maximum positive displacement, given velocity $v_x = 32.0 t -

1. **State the problem:** A ball is projected horizontally from a height of 80 m with an initial velocity of 20 m/s. We need to find how far from the base of the projection point i

1. **Problem statement:** A projectile is launched at an angle of $30^\circ$ with an initial velocity of $20$ m/s. We need to find the time of flight. 2. **Formula used:** The time