🔭 physics

1. **Problem statement:** Calculate the amount of heat energy (in kJ) delivered by an electric boiler with a power rating of 7.5 kW over a period of one hour.

1. **Problem statement:** A flowerpot falls past a window 1.9 m tall in 0.20 s. We need to find the height above the top of the window from which the flowerpot was dropped. 2. **Kn

1. **State the problem:** We have a frisbee thrown with initial velocity 40 ft/s from a height of 5 ft. The height after $t$ seconds is given by the function $$h(t) = -16t^2 + 40t

1. **Problem statement:** A bucket filled with water is tied to a string of length 50 cm and rotated in a vertical circle. We need to find the minimum angular speed at the highest

1. **Problem statement:** An object of mass 0.5 kg is rotated in a horizontal circle by a string 1.0 m long. The maximum tension the string can withstand before breaking is 50 N. W

1. **Problem statement:** Repeat part a for an object thrown upwards on Mars where gravity $g = 3.7 \text{ m/s}^2$.

1. **State the problem:** We are given the position function for an object under gravity:

1. **State the problem:** Calculate the height $S(t)$ of an object thrown upwards with initial velocity $v_0=28$ m/s from an initial height $h_0=3$ m after $t=2$ seconds, under gra

1. **Stating the problem:** We want to find the velocity and height of an object in motion, typically under gravity. 2. **Formulas used:**

1. **Stating the problem:** We are given the position function of an object moving under constant acceleration:

1. The problem is to understand and analyze the function describing vertical motion under gravity on Mars: $$y(t) = -\frac{1}{2}gt^2 + v_0 t + h_0$$ where $g$ is the acceleration d

1. **State the problem:** We need to find the unit rate of speed (kilometers per hour) for two birds: a bald eagle and a peregrine falcon.

1. **Problem statement:** Radon-222 decays exponentially with a half-life of 4 days. 2. **Formula for exponential decay:**

1. **State the problem:** We need to find how long the catcher has to get in position to catch the ball before it hits the ground. The height of the ball is given by the quadratic

1. **State the problem:** We have a radioactive isotope with an initial mass of 250 grams that halves every 10 years. We want to find the remaining mass after 6 years. 2. **Formula

1. **State the problem:** We are given the height function of a baseball popped up as \(b(t) = 80t - 16t^2 + 3.5\). We need to find how long the catcher has to get in position befo

1. **State the problem:** Determine whether the given scenarios represent examples of work done. 2. **Recall the definition of work:** Work is done when a force causes displacement

1. The problem asks if we need to do anything with the kinetic friction coefficient 0.29. 2. The kinetic friction coefficient, usually denoted as $\mu_k$, is a constant that quanti

1. **State the problem:** We need to find the force required to start moving a 35 kg crate given the coefficient of static friction $\mu_s = 0.35$. 2. **Formula used:** The force t

1. **Problem statement:** Find the current $I(t)$ in amperes at time $t$ seconds after the switch is closed in an RL circuit with voltage $E=60$, inductance $L=1$, resistance $R=30

1. **Problem statement:** Find the average velocity over given intervals and the instantaneous velocity at $t=8$ for the displacement function